Schur-Weyl Categories and Non-quasiclassical Weyl Type Formula
Gurevich, D. · Mriss, Z.
Original · EN
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 and compute its dimension. The functor V is an analogue of the well-known Schur functor. The category generated by the objects 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()={ ᵢ≤}, where ᵢ are the eigenvalues of this operator.
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