On the tensor product of two basic representations of $U_v(\hat{sl}_e)$
| dc.creator | Ariki, Susumu | |
| dc.creator | Kreiman, Victor | |
| dc.creator | Tsuchioka, Shunsuke | |
| dc.date | 2006-06-02 | |
| dc.date | 2007-12-20 | |
| dc.date.accessioned | 2026-07-07T08:50:26Z | |
| dc.date.available | 2026-07-07T08:50:26Z | |
| dc.description | Let $\{B(Λ_m)|m\in\Z/e\Z\}$ be the set of level one $\mathfrak{g}(A^{(1)}_{e-1})$-crystals, and consider the realization of $B(Λ_m)$ using $e$-restricted partitions. We prove a purely Young diagrammatic criterion for an element of $B(Λ_0)^{\otimes d_1}\otimes B(Λ_m)^{\otimes d_2}$ to be in the component $B(d_1Λ_0+d_2Λ_m)$. As an application, we give a non-recursive characterization of simple modules of the Hecke algebra of type $B$. In the course of the proof, we also obtain a combinatorial description of the second type of Kashiwara's Demazure crystal in $B(Λ_m)$. | |
| dc.description | 52 pages, (v2,v3) typos and reference numbers corrected, (v4,v5) minor revision | |
| dc.identifier | https://arxiv.org/abs/math/0606044 | |
| dc.identifier | http://arxiv.org/abs/math/0606044 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144606 | |
| dc.subject | Representation Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | On the tensor product of two basic representations of $U_v(\hat{sl}_e)$ | |
| dc.type | text |