LIST OF PUBLICATIONS OF NEDIALKA ILIEVA STOILOVA

  1. K. Tzerova, M. Sarafova, R. Gacheva, N. Ilieva, N.Balabanov, Neutron methods for measurement of the thickness of etalon coverings.
    Nauchni Trudove, University of Plovdiv, 23, 59 (1985).
  2. T.D. Palev, N.I. Stoilova, Finite-dimensional representations of the Lie superalgebra gl(2/2) in a gl(2) + gl(2) basis. II.Nontypical representations.
    Journ. Math. Phys. 31 953-988 (1990).
  3. T.D. Palev, N.I. Stoilova, Finite-dimensional representations of the basic Lie superalgebra A(1/1) in a sl(2) + sl(2) basis.
    Preprint INRNE-TH-90, Sofia (1990).
  4. T.D. Palev, N.I. Stoilova, Osp(3/2) noncanonical quantum oscillator.
    Sakharov Memorial Lectures in Physics, p.283-290, (Eds. L.V.Keldysh and V. Ya. Feinberg, Nove Sci. Publ. New York), Proceedings of the First International Sakharov Conference on Physics, Moscow, May 27-31, 1991.
  5. T.D. Palev, N.I. Stoilova, Classification of all three-dimension noncanonical quantum oscillators generating classical Lie superalgebras.
    Classical and Quantum Systems - Foundations and Symmetries, p.318-321, (Eds. H.D.Doebner, W.Schehrer, Schroeck, World Sci Pub. 1993). Proceedings of the II International Wigner Symposium, July 16-20, 1991, Goslar, Germany.
  6. N.A. Ky, T.D. Palev, N.I. Stoilova, Transformations of some induced osp(3/2) modules in an so(3) + sp(2) basis.
    Journ. Math. Phys. 33, 1841-1863 (1992).
  7. T.D. Palev, N.I. Stoilova, Wigner quantum systems: Noncanonical osp(3/2) Oscillator.
    Preprint Concordia University 1/92, Montreal (1992).
  8. N.I. Stoilova, Wigner quantum systems and representations of Lie superalgebras.
    Ph. D. Thesis, Sofia, Bulgaria (in Bulgarian).
  9. T.D. Palev, N.I. Stoilova, On a Possible algebra morphism of Uq[osp(1/2n)] onto the deformed oscillator algebra Wq(n).
    Lett. Math. Phys. 28, 187-193 (1993) and hep-th/9303142.
  10. T.D. Palev, N.I. Stoilova, Finite-dimensional representations of the quantum superalgebra Uq[gl(3/2)] in a reduced Uq[gl(3/2)] $\supset$ Uq[gl(3/1)] $\supset$ Uq[gl(3)] basis.
    J. Phys. A 26, 5867-5872 (1993) and hep-th/9305136.
  11. T.D. Palev, N.I. Stoilova, J. Van der Jeugt, Finite-dimensional representations of the quantum superalgebra Uq[gl(n/m)] and related q-identities.
    Commun. Math. Phys. 166 367-378 (1994) and hep-th/9306149.
  12. T.D. Palev, N.I. Stoilova, Wigner quantum oscillators.
    J.Phys. A 27, 977-983 (1994) and hep-th/9307102.
  13. T.D. Palev, N.I. Stoilova, Wigner quantum oscillators. Osp(3/2) oscillators.
    J.Phys. A 27 7387-7401 (1994) and hep-th/9405125.
  14. T.D. Palev and N.I. Stoilova, Wigner quantum oscillators.
    Proceedings of the Yamada Conference XL and XX ICGTMP, Toyanoka, Japan, July 4-9, 1994 (Ed. A. Arima, T. Eguchi, N. Nakanishi, World Scientific Pub. Co Pte, 1995), p. 386-389.
  15. Nguyen Anh Ky, N.I. Stoilova, Finite-dimensional representations of the quantum superalgebra Uq[gl(2/2)]. II: Nontypical representations of generic q.
    Journ. Math. Phys. 36 N 10, 5979-6003 (1995) and hep-th/9411098.
  16. T.D. Palev and N.I. Stoilova, Unitarizable representations of the deformed para-Bose superalgebra Uq[osp(1/2)] at roots of 1.
    J. Phys. A 28 7275-7285 (1995) and q-alg/9507026 .
  17. T.D. Palev and N.I. Stoilova, New solutions of the Yang-Baxter equation based on root of 1 representations of the para-Bose superalgebra Uq[osp(1/2)].
    J. Phys. A 29 709-719 (1996) and q-alg/9507027.
  18. T.D. Palev and N.I. Stoilova, Many-body Wigner quantum systems.
    Journ. Math. Phys. 38 2506-2523 (1997) and hep-th/9605011.
  19. T.D. Palev and N.I. Stoilova, Representations of the quantum algebra Uq[gl(∞)].
    Preprint Univ. of Queensland, UQMATH-arc-9620.
  20. M.D.Gould and N.I.Stoilova, Casimir invariants and characteristic identities for gl(∞).
    Journ. Math. Phys. 38 4783-4793 (1997) and physics/9612009.
  21. T.D. Palev and N.I. Stoilova, Highest weight representations of the quantum algebra Uh(gl∞ ).
    J. Phys. A 30 L699-L705 (1997) and q-alg/9704001.
  22. T.D. Palev and N.I. Stoilova, Highest weight irreducible representations of the quantum algebra Uh(A∞ ).
    Journ. Math. Phys. 39 5832-5849 (1998); q-alg/9709004 and math.QA/9807157 - an extended version, containing all proofs.
  23. M.D. Gould and N.I. Stoilova, Eigenvalues of Casimir operators for gl(m/∞).
    J. Phys. A 32 391-399 (1999) and physics/9709033.
  24. T.D. Palev and N.I. Stoilova, Representations of the quantum algebra Uh(A∞ ).
    "Lie Theory and Its Applications in Physics II" 338-349
    (Proceedings of the II International Workshop on Lie Theory and Its Applications in Physics, August 17-20, 1997 Arnold Sommerfeld Institute, Technical University of Clausthal), Eds. H.-D. Doebner, V.K. Dobrev and J. Hilgert, World Sci, Singapore, 1998; ISBN 981-02-3539-9.
  25. T.D. Palev and N.I. Stoilova, Highest weight irreducible representations of the Lie superalgebra gl(1/∞).
    Journ. Math. Phys. 40 1574-1594 (1999) and math-ph/9809024.
  26. T.D. Palev and N.I. Stoilova, A description of the quantum superalgebra Uq[sl(n+1|m)] via creation and annihilation generators.
    J. Phys. A 32 1053-1064 (1999) and math.QA/9811141.
  27. T.D. Palev, N.I. Stoilova and J. Van der Jeugt, A new description of the quantum superalgebra Uq[sl(n+1|m)] and related Fock representations.
    ``Quantum Theory and Symmetries'', (Proceedings of the International Symposium on Quantum Theory and Symmetries, July, 18-22, 1999, Goslar, Germany), Eds. H.-D. Doebner, V.K. Dobrev, J.-D. Hennig and W. Lucke, 437-441, World Sci, Singapore and math.QA/9911169.
  28. T.D. Palev, N.I. Stoilova and J. Van der Jeugt, Fock representations of the superalgebra sl(n+1|m), its quantum analogue Uq[sl(n+1|m)] and related quantum statistics.
    J. Phys. A 33 2545-2553 (2000) and math-ph/0002041.
  29. T.D. Palev and N.I. Stoilova, Wigner quantum system, pp. 358-360.
    Concise Encyclopedia of Sypersymmetry and noncommutative structures in mathematics and physics, Eds. J. Bagger, St. Duplij, W. Siegel, Kluwer Academic Publishers, Dordrecht, 2001, ISBN 1-4020-1338-8.
  30. T.D. Palev, N.I. Stoilova and J. Van der Jeugt, Jacobson generators of the quantum superalgebra Uq[sl(n+1|m)] and Fock representations.
    Journ. Math. Phys. 43 1646-1663 (2002) and math.QA/0111289.
  31. T.D. Palev and N.I. Stoilova, Wigner Quantum Systems (Lie superalgebraic approach).
    Rep. Math. Phys. 49 395-404 (2002) and hep-th/0111011.
  32. T.D. Palev, N.I. Stoilova and J. Van der Jeugt, Jacobson generators of (quantum) sl(n+1|m). Related statistics,
    Proceedings of Institute of Mathematics of NAS of Ukraine, volume 43. Eds. A.G. Nikitin, V.M. Boyko and R.O. Popovych (Institute of Mathematics, Kyiv, 2002; ISBN 966-02-2488-5), 478-485.
  33. T.D. Palev, N.I. Stoilova and J. Van der Jeugt, Deformed Jacobson generators of the algebra Uq[sl(n+1)] and their Fock representations.
    Proceedings of the IInd International Symposium Quantum Theory and Symmetries. Eds. E. Kapuscik and A. Horzela (World Scientific, Singapore, 2002; ISBN 981-02-4887-3), 521-526 and math.QA/0111289.
  34. H.-D. Doebner, T.D. Palev and N.I. Stoilova, On deformed Clifford Clq(n|m) and orthosymplectic Uq[osp(2n+1|2m)] superalgebras and their root of unity representations.
    J. Phys. A 35 9367-9380 (2002) and math.QA/0210340.
  35. R.C. King, T.D. Palev, N.I. Stoilova and J. Van der Jeugt, The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator.
    J. Phys. A 36 4337-4362 (2003) and hep-th/0304136; hep-th/0210164 - an extended version of the paper.
  36. T.D. Palev, N.I. Stoilova and J. Van der Jeugt, Microscopic and macroscopic properties of A-superstatistics.
    J. Phys. A 36 7093-7112 (2003) and math-ph/0306032.
  37. R.C. King, T.D. Palev, N.I. Stoilova and J. Van der Jeugt, A non-commutative n-particle 3D Wigner quantum oscillator.
    J. Phys. A 36 11999-12019 (2003) and hep-th/0310016.
  38. R.C. King, T.D. Palev, N.I. Stoilova and J. Van der Jeugt, On the N-particle Wigner quantum oscillator: non-commutative coordinates and particle localization.
    in: Lie Theory and Its Applications in Physics V, Proceedings of the Fifth International Workshop, Varna, Bulgaria 16 - 22 June 2003 . Eds. H.-D. Doebner and V.K. Dobrev (World Scientific, Singapore, 2004; ISBN 981-238-936-9), 327-341.
  39. N.I. Stoilova and J. Van der Jeugt, A classification of generalized quantum statistics associated with classical Lie algebras.
    J. Math. Phys. 46 033501-1-033501-16 (2005) and math-ph/0409002.
  40. R.C. King, T.D. Palev, N.I. Stoilova and J. Van der Jeugt, The N-particle Wigner quantum oscillator: non-commutative coordinates and physical properties, in: Group Theoretical Methods in Physics. Institute of Physics Conference Series 185. Eds. G.S. Pogosyan, L.E. Vicent and K.B. Wolf (IOP Publishing, Bristol, 2005; ISBN 0-7503-1008-1), 545-550.
  41. N.I. Stoilova and J. Van der Jeugt, Lie algebraic generalization of quantum statistics, in: Group Theoretical Methods in Physics. Institute of Physics Conference Series 185. Eds. G.S. Pogosyan, L.E. Vicent and K.B. Wolf (IOP Publishing, Bristol, 2005; ISBN 0-7503-1008-1), 509-514.
  42. N.I. Stoilova and J. Van der Jeugt, Fundamental fermions fit inside one su(1|5) irreducible representation.
    Jnt. J. Theor. Phys. 44 , 1157-1165 (2005) and math-ph/0411213 .
  43. N.I. Stoilova and J. Van der Jeugt, A classification of generalized quantum statistics associated with basic classical Lie superalgebras.
    J. Math. Phys. 46 , 113504-113505 (2005) and math-ph/0504013.
  44. N.I. Stoilova and J. Van der Jeugt, Solutions of the compatibility conditions for a Wigner quantum oscillator.
    J. Phys. A 38 , 9681-9688 (2005) and math-ph/0506054.
  45. N.I. Stoilova and J. Van der Jeugt, Lie superalgebraic framework for generalization of quantum statistics.
    Bulg. J. Phys. 33 (s2) , 292-300 (2006).
  46. R.C. King, N.I. Stoilova and J. Van der Jeugt, Representations of the Lie Superalgebra gl(1|n) in a Gel'fand-Zetlin Basis and Wigner Quantum Oscillators.
    J. Phys. A 39 , 5763-5785 (2006) and hep-th/0602169.
  47. S. Lievens , N.I. Stoilova and J. Van der Jeugt, Harmonic oscillators coupled by springs: discrete solutions as a Wigner Quantum System.
    J. Math. Phys. 47 , 113504 (2006) (23 pages) and hep-th/0606192.
  48. N.I. Stoilova and J. Van der Jeugt, A classification of generalized quantum statistics associated with the exceptional Lie (super)algebras,
    J. Math. Phys. 48 , 043504 (2007) (18 pages) math-ph/0611085.
  49. S. Lievens , N.I. Stoilova and J. Van der Jeugt, On the eigenvalue problem for arbitrary odd elements of the Lie superalgebra gl(1|n) and applications.
    J. Phys. A: Math. Theor. 40 , 3869-3888, (2007) and math-ph/0701013.
  50. S. Lievens , N.I. Stoilova and J. Van der Jeugt, The paraboson Fock space and unitary irreducible representations of the Lie superalgebra osp(1|2n).
    Commun. Math. Phys. 281 , 805-826 (2008) and arXiv:0706.4196[hep-th].
  51. S. Lievens , N.I. Stoilova and J. Van der Jeugt, Harmonic oscillator chains as Wigner Quantum Systems: periodic and fixed wall boundary conditions in gl(1|n) solutions.
    J. Math. Phys. 49 , 073502 (22 pages) (2008) and arXiv:0709.0180[hep-th].
  52. S. Lievens , N.I. Stoilova and J. Van der Jeugt, Unitary representations of the Lie superalgebra osp(1|2n) and parabosons.
    Bulg. J. Phys. 35 (s1), 403-414, (2008).
  53. N.I. Stoilova and J. Van der Jeugt, Algebraic generalization of quantum statistics.
    J. Phys: Conf. Series 128 , 012061 (13 pp), (2008)
  54. S. Lievens, N.I. Stoilova and J. Van der Jeugt, A linear chain of interacting harmonic oscillators: solutions as a Wigner quantum system.
    J. Phys: Conf. Series 128 , 012028 (11 pp), (2008)
  55. S. Lievens, N.I. Stoilova and J. Van der Jeugt, A class of unitary irreducible representations of the Lie superalgebra osp(1|2n).
    Journal of Generalized Lie Theory and Applications 2 , N 3, 206-210 (2008) ISSN 1736-5279.
  56. N.I. Stoilova and J. Van der Jeugt, The parafermion Fock space and explicit so(2n+1) representations.
    J. Phys. A: Math. Theor. 41 075202 (13 pp), (2008) and arXiv:0712.1485[hep-th].
  57. N.I. Stoilova and J. Van der Jeugt, Parafermions, parabosons and representations of so(∞) and osp(1|∞),
    Int. J. Math. 20 , N 6, 693-715 (2009) and arXiv:0801.3909[hep-th].
  58. R. Chakrabarti, N.I. Stoilova and J. Van der Jeugt, Representations of the orthosymplectic Lie superalgebra osp(1|4) and paraboson coherent states,
    J. Phys. A: Math. Theor. 42 085207 (16pp) (2009) and arXiv:0811.0281v1 [math-ph].
  59. R.C. King, N.I. Stoilova and J. Van der Jeugt, Representations of the Lie Superalgebra gl(1|n) and Wigner Quantum Oscillators,
    in: Group Theoretical Methods in Physics 2006, Eds. J.L. Birman, S. Catto, B. Nicolescu, (Canopus Publishing Limited 2009, ISBN 978-0-9549846-8-7), 340-344.
  60. S. Lievens , N.I. Stoilova and J. Van der Jeugt, Finite-dimensional solutions of coupled harmonic oscillator quantum systems,
    in: Group Theoretical Methods in Physics 2006, Eds. J.L. Birman, S. Catto, B. Nicolescu, (Canopus Publishing Limited 2009, ISBN 978-0-9549846-8-7), 363-367.
  61. R. Chakrabarti, N.I. Stoilova and J. Van der Jeugt, Paraboson Coherent States,
    Physics of Atomic Nuclei 73 , No. 2, 269-275 (2010), ISSN 1063-7788.
  62. N.I. Stoilova and J. Van der Jeugt, Parabosons, Parafermions, and Explicit Representations of Infinite-Dimensional Algebras,
    Physics of Atomic Nuclei 73 , No. 3, 533-540 (2010), ISSN 1063-7788.
  63. N.I. Stoilova and J. Van der Jeugt, Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n),
    J. Math. Phys. 51 093523 (15pp) (2010) and arXiv:1004.2381 [math-ph].
  64. N.I. Stoilova and J. Van der Jeugt, An exactly solvable spin chain related to Hahn polynomials,
    SIGMA 7 033 (13pp) (2011) and arXiv:1101.4469 [math-ph].
  65. E.I. Jafarov, N.I. Stoilova and J. Van der Jeugt, Finite oscillator models: the Hahn oscillator,
    J. Phys. A: Math. Theor. 44 265203 (15pp) (2011) and arXiv:1101.5310 [math-ph].
  66. E.I. Jafarov, N.I. Stoilova and J. Van der Jeugt, The su(2)α Hahn oscillator and a discrete Hahn-Fourier transform,
    J. Phys. A: Math. Theor. 44 355205 (18pp) (2011) and arXiv:1106.1083 [math-ph].
  67. N.I. Stoilova and J. Van der Jeugt, Explicit representations of classical Lie superalgebras in a Gel'fand-Zetlin basis,
    Banach Center Publications 93 (2011), 83-93, ISBN 978-83-86806-11-9.
  68. E.I. Jafarov, N.I. Stoilova and J. Van der Jeugt, Deformed su(1,1) algebra as a model for quantum oscillators,
    SIGMA 8 025 (15pp) (2012) and arXiv:1202.3541 [math-ph].
  69. N.I. Stoilova, The parastatistics Fock space and explicit Lie superalgebra representations,
    J. Phys. A: Math. Theor. 46 475202 (14pp) (2013) and arXiv:1311.4042 [math-ph].
  70. E.I. Jafarov, N.I. Stoilova and J. Van der Jeugt, The u(2)α and su(2)α Hahn harmonic oscillators,
    Bulg. J. Phys. 40 115-120 (2013).
  71. E.I. Jafarov, N.I. Stoilova and J. Van der Jeugt, On a pair of difference equations for the 4 F3 type orthogonal polynomials and related exactly-solvable quantum systems,
    in Lie Theory and Its Applications in Physics, ed. V. Dobrev, Springer Proceedings in Mathematics and Statistics, 111 291-300 (2014) (Springer, Tokyo, Heidelberg, ISSN 2194-1009, ISBN 978-4-431-55284-0)
  72. N.I. Stoilova and J. Van der Jeugt, Explicit infinite-dimensional representations of the Lie superalgebra osp(2m + 1|2n) and the parastatistics Fock space,
    J. Phys. A: Math. Theor. 48 155202 (16pp) (2015).
  73. N.I. Stoilova, Generalized Quantum Statistics and Lie (Super)Algebras,
    9th Int. Physics Conference of the Balkan Physical Union (BPU-9), AIP Conference Proceedings 1722, 100004-1--100004-4 (2016), doi: 10. 1063/1.4944182 and arXiv:1512.05076.
  74. N.I. Stoilova and J. Van der Jeugt, Gel'fand-Zetlin basis for a class of representations of the Lie superalgebra gl(∞|∞),
    J. Phys. A: Math. Theor. 49 165204 (21pp) (2016).
  75. N.I. Stoilova and J. Van der Jeugt, The parastatistics Fock space and explicit infinite-dimensional representations of the Lie superalgebra osp(2m+1|2n),
    in Lie Theory and Its Applications in Physics, ed. V. Dobrev, Springer Proceedings in Mathematics and Statistics, 191 169-180 (2016) (Springer, Tokyo, Heidelberg, ISSN 2194-1009, ISBN 978-981-10-2635-5)
  76. N.I. Stoilova, Representations of basic classical Lie superalgebras and generalized quantum statistics,
    D.Sc. Thesis, Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences (2016).
  77. N.I. Stoilova, J. Thierry-Mieg and J. Van der Jeugt, Extension of the osp(m|n) ~ so(m-n) correspondence to the infinite-dimensional chiral spinors and self dual tensors,
    J. Phys. A: Math. Theor. 50 155201 (21 pp) (2017).
  78. N.I. Stoilova and J. Van der Jeugt, Lie superalgebraic approach to quantum statistics. osp(3|2) Wigner quantum oscillator,
    Bulg. J. Phys. 44 1-8 (2017).