Jun 20, 2024
Atoms and charge beyond type A
Algebraic Geometry and Number Theory Seminar
Date: June 20, 2024 |
1:00 pm –
2:30 pm
Speaker:
Jacinta Perez Gavilan Torres, Jagiellonian University, Krakow
Location: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Language:
English
Kostka-Foulkes polynomials are q-analogues of weight multiplicities for irreducible representations of semi-simple finite-dimensional complex Lie algebras. They appear in various contexts in representation theory; in particular they are affine Kazdhan-Lusztig polynomials and therefore have positive coefficients. In type A, that is, for the special linear Lie algebra, a positive combinatorial formula has been known since 1978. However, in general, the problem is still wide open. I will give a historical introduction to the problem of finding a positive combinatorial formula for Kostka-Foulkes polynomials beyond type A. Then I will present some joint results with Leonardo Patimo in this direction – in particular such a formula for type B2/C2.
