Schur-Weyl Categories and Non-quasiclassical Weyl Type Formula
| dc.creator | Gurevich, D. | |
| dc.creator | Mriss, Z. | |
| dc.date | 1999-11-18 | |
| dc.date.accessioned | 2026-07-07T05:31:40Z | |
| dc.date.available | 2026-07-07T05:31:40Z | |
| dc.description | To a vector space V equipped with a non-quasiclassical involutary solution of the quantum Yang-Baxter equation and a partition $λ$, we associate a vector space $\Vl$ and compute its dimension. The functor $V\mapsto \Vl$ is an analogue of the well-known Schur functor. The category generated by the objects $\Vl$ is called the Schur-Weyl category. We suggest a way to construct some related twisted varieties looking like orbits of semisimple elements in sl(n)^*. We consider in detail a particular case of such "twisted orbits", namely the twisted non-quasiclassical hyperboloid and we define the twisted Casimir operator on it. In this case, we obtain a formula looking like the Weyl formula, and describing the asymptotic behavior of the function $N(\la)=\{\sharp \la_i\leq\la\}$, where $\la_i$ are the eigenvalues of this operator. | |
| dc.description | Latex file, 35 pages | |
| dc.identifier | https://arxiv.org/abs/math/9911139 | |
| dc.identifier | http://arxiv.org/abs/math/9911139 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79432 | |
| dc.subject | Quantum Algebra | |
| dc.title | Schur-Weyl Categories and Non-quasiclassical Weyl Type Formula | |
| dc.type | text |