Affine sl_p controls the representation theory of the symmetric group and related Hecke algebras
| dc.creator | Grojnowski, I. | |
| dc.date | 1999-07-21 | |
| dc.date.accessioned | 2026-07-07T05:29:58Z | |
| dc.date.available | 2026-07-07T05:29:58Z | |
| dc.description | In this paper we prove theorems that describe how the representation theory of the affine Hecke algebra of type A and of related algebras such as the group algebra of the symmetric group are controlled by integrable highest weight representations of the characteristic zero affine Lie algebra \hat{sl}_l. In particular we parameterise the representations of these algebras by the nodes of the crystal graph, and give various Hecke theoretic descriptions of the edges. As a consequence we find for each prime p a basis of the integrable representations of \hat{sl}_l which shares many of the remarkable properties, such as positivity, of the global crystal basis/canonical basis of Lusztig and Kashiwara. This {\it $p$-canonical basis} is the usual one when p = 0, and the crystal of the p-canonical basis is always the usual one. The paper is self-contained, and our techniques are elementary (no perverse sheaves or algebraic geometry is invoked). | |
| dc.identifier | https://arxiv.org/abs/math/9907129 | |
| dc.identifier | http://arxiv.org/abs/math/9907129 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78850 | |
| dc.subject | Representation Theory | |
| dc.title | Affine sl_p controls the representation theory of the symmetric group and related Hecke algebras | |
| dc.type | text |