On Isomorphisms of Certain Functors for Cherednik Algebras
نویسنده
چکیده
Bezrukavnikov and Etingof introduced some functors between the categories O for rational Cherednik algebras. Namely, they defined two induction functors Indb, indλ and two restriction functors Resb, resλ. They conjectured that one has functor isomorphisms Indb ∼= indλ,Resb ∼= resλ. The goal of this paper is to prove this conjecture.
منابع مشابه
Monodromy of Partial Kz Functors for Rational Cherednik Algebras
1.1. Shan has proved that the categories Oc(Wn) for rational Cherednik algebras of type Wn = W (G(`, 1, n)) = Snn(μ`) with n varying, together with decompositions of the parabolic induction and restriction functors of Bezrukavnikov-Etingof, provide a categorification of an integrable s̃le Fock space representation F(m), [18]. The parameters m ∈ Z` and e ∈ N ∪ {∞} arise from the choice of paramet...
متن کاملFunctoriality of Rieffel’s Generalised Fixed-Point Algebras for Proper Actions
We consider two categories of C-algebras; in the first, the isomorphisms are ordinary isomorphisms, and in the second, the isomorphisms are Morita equivalences. We show how these two categories, and categories of dynamical systems based on them, crop up in a variety of C-algebraic contexts. We show that Rieffel’s construction of a fixed-point algebra for a proper action can be made into functor...
متن کاملFunctors Induced by Cauchy Extension of C$^ast$-algebras
In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by ...
متن کاملar X iv : m at h / 05 11 38 4 v 2 [ m at h . R T ] 1 9 Ju n 20 06 Applications of BGP - reflection functors : isomorphisms of cluster algebras ∗
Given a symmetrizable generalized Cartan matrix A, for any index k, one can define an automorphism associated with A, of the field Q(u1, · · · , un) of rational functions of n independent indeterminates u1, · · · , un. It is an isomorphism between two cluster algebras associated to the matrix A (see section 4 for precise meaning). When A is of finite type, these isomorphisms behave nicely, they...
متن کامل1 5 N ov 2 00 5 Applications of BGP - reflection functors : isomorphisms of cluster algebras ∗
Given a symmetrizable generalized Cartan matrix A, for any index k, one can define an automorphism associated with A, of the field Q(u1, · · · , un) of rational functions of n independent indeterminates u1, · · · , un. It is an isomorphism between two cluster algebras associated to the matrix A (see section 4 for precise meaning). When A is of finite type, these isomorphisms behave nicely, they...
متن کامل