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Schur-Weyl Categories and Non-quasiclassical Weyl Type Formula | | D. Gurevich
; Z. Mriss
; | | Date: |
18 Nov 1999 | | Subject: | Quantum Algebra | math.QA | | Abstract: | To a vector space V equipped with a non-quasiclassical involutary solution of the quantum Yang-Baxter equation and a partition $lambda$, we associate a vector space $Vl$ and compute its dimension. The functor $Vmapsto Vl$ 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 $N(la)={sharp la_ileqla}$, where $la_i$ are the eigenvalues of this operator. | | Source: | arXiv, math.QA/9911139 | | Services: | Forum | Review | PDF | Favorites | |
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