6 February 2020, 13:15 (EET), Hall 300, INRNE

• Roy Oste (Ghent University, Belgium)
• Title: A Howe duality deformation using reflection groups
• Abstract: Our starting point is the multiplicity-free decomposition of the space of polynomials into spherical harmonics under the joint action of the Howe dual pair (O(n),sl(2)). The analogue for spinor-valued polynomials is governed by the pair(Pin(n),osp(1|2)). Using a finite reflection group and its associated rational Cherednik algebra, which acts on polynomials through the Dunkl operator realization, one obtains a deformation of these decompositions. In this way, interesting algebraic structures appear resembling Z_2^n-graded algebras. The goal of this talk is to introduce these deformations and to have a closer look at the specific example of the dihedral groups and some ongoing research questions.