A Quiver Construction of Symmetric Crystals
| dc.creator | Enomoto, Naoya | |
| dc.date | 2008-06-23 | |
| dc.date | 2008-08-04 | |
| dc.date.accessioned | 2026-07-07T09:54:11Z | |
| dc.date.available | 2026-07-07T09:54:11Z | |
| dc.description | In the recent papers with Masaki Kashiwara, the author introduced the notion of symmetric crystals and presented the Lascoux-Leclerc-Thibon-Ariki type conjectures for the affine Hecke algebras of type $B$. Namely, we conjectured that certain composition multiplicities and branching rules for the affine Hecke algebras of type $B$ are described by using the lower global basis of symmetric crystals of $V_θ(λ)$. In this paper, we prove the existence of crystal bases and global bases of $V_θ(0)$ for any symmetric quantized Kac-Moody algebra by using a geometry of quivers (with a Dynkin diagram involution). This is analogous to George Lusztig's geometric construction of $U_v^-$ and its lower global basis. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/0806.3615 | |
| dc.identifier | http://arxiv.org/abs/0806.3615 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166220 | |
| dc.subject | Representation Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | A Quiver Construction of Symmetric Crystals | |
| dc.type | text |