Some Geometry and Combinatorics around the Representations of Cherednik Algebras
Presenter
January 25, 2013
Keywords:
- deformation quantization
- derived categories
- D-modules
- noncommutative algebraic geometry
- resolution of singularities
- symplectic singularities
- symplectic varieties
- Coxeter groups
- Catalan numbers
- reflection groups
- Cherednik algebra
- algebraic combinatorics
MSC:
- 13D09
- 13D10
- 13Dxx
- 13-xx
- 14Fxx
- 14F05
- 14F10
- 14A22
- 16Txx
- 16T05
- 16T10
- 16T30
- 53Dxx
Abstract
The representation theory of Cherednik algebras has connections with parts of geometry and combinatorics. Topics include resolving symplectic singularities, realization of phase spaces of some classical integrable systems, positivity for symmetric functions and the numerology of reflection groups. I will discuss a couple of these. No prior knowledge will be assumed.