Abstract
We formulate a q-Schur algebra associated with an arbitrary W-invariant finite set Xf of integral weights for a complex simple Lie algebra with Weyl group W. We establish a q-Schur duality between the q-Schur algebra and Hecke algebra associated with W. We then realize geometrically the q-Schur algebra and duality and construct a canonical basis for the q-Schur algebra with positivity. With suitable choices of Xf in classical types, we recover the q-Schur algebras in the literature. Our q-Schur algebras are closely related to the category O, where the type G2 is studied in detail.
| Original language | English |
|---|---|
| Pages (from-to) | 129-160 |
| Number of pages | 32 |
| Journal | Journal of the Institute of Mathematics of Jussieu |
| Volume | 21 |
| Issue number | 1 |
| DOIs | |
| State | Published - 19 Jan 2022 |
Keywords
- Hecke algebras; q-Schur algebras; canonical basis