Crystal bases and two-sided cells of quantum affine algebras
| dc.creator | Beck, Jonathan | |
| dc.creator | Nakajima, Hiraku | |
| dc.date | 2002-12-18 | |
| dc.date.accessioned | 2026-07-07T04:53:53Z | |
| dc.date.available | 2026-07-07T04:53:53Z | |
| dc.description | Let $\g$ be an affine Kac-Moody Lie algebra. Let $\U^+$ be the positive part of the Drinfeld-Jimbo quantum enveloping algebra associated to $\g$. We construct a basis of $\U^+$ which is related to the Kashiwara-Lusztig global crystal basis (or canonical basis) by an upper triangular matrix (with respect to an explicitly defined ordering) with 1's on the diagonal and with above diagonal entries in $q_s^{-1} \Z[q_s^{-1}]$. Using this construction we study the global crystal basis $\B(\Um)$ of the modified quantum enveloping algebra defined by Lusztig. We obtain a Peter-Weyl like decomposition of the crystal $\B(\Um)$ (Theorem 4.18), as well as an explicit description of two-sided cells of $\B(\Um)$ and the limit algebra of $\Um$ at $q=0$ (Theorem 6.45). | |
| dc.description | 50 pages | |
| dc.identifier | https://arxiv.org/abs/math/0212253 | |
| dc.identifier | http://arxiv.org/abs/math/0212253 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66029 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 17B37 | |
| dc.title | Crystal bases and two-sided cells of quantum affine algebras | |
| dc.type | text |