Cuspidal Representations of Rational Cherednik Algebras
نویسنده
چکیده
We study those finite dimensional quotients of the rational Cherednik algebra at t = 0 that are supported at a point of the centre. It is shown that each such quotient is Morita equivalent to a certain “cuspidal” quotient of a rational Cherednik algebra associated to a parabolic subgroup of W .
منابع مشابه
Unitary Representations of Rational Cherednik Algebras
We study unitarity of lowest weight irreducible representations of rational Cherednik algebras. We prove several general results, and use them to determine which lowest weight representations are unitary in a number of cases. In particular, in type A, we give a full description of the unitarity locus (justified in Subsection 5.1 and the appendix written by S. Griffeth), and resolve a question b...
متن کاملRepresentations of rational Cherednik algebras of rank 1 in positive characteristic
Let Γ ⊂ SL2(C) be a finite subgroup, and r be the number of conjugacy classes of Γ. Let D be the algebra of polynomial differential operators in one variable with complex coefficients. In the paper [CBH98], CrawleyBoevey and Holland introduced an r-parameter family of algebras Ht,c1,...,cr−1 over C, which is a universal deformation of the semidirect product algebra CΓ ⋉ D. They also described t...
متن کاملQuasiharmonic Polynomials for Coxeter Groups and Representations of Cherednik Algebras
We introduce and study deformations of finite-dimensional modules over rational Cherednik algebras. Our main tool is a generalization of usual harmonic polynomials for each Coxeter groups — the so-called quasiharmonic polynomials. A surprising application of this approach is the construction of canonical elementary symmetric polynomials and their deformations for all Coxeter groups.
متن کاملApplications of Procesi Bundles to Cherednik Algebras
In this talk we describe some applications of Procesi bundles that appeared in Gufang’s talk to type A Rational Cherednik algebras introduced in Jose’s talk. We start by recalling Procesi bundles, quantum Hamiltonian reductions, and Cherednik algebras. Then we apply Procesi bundles to relating the spherical Rational Cherednik algebras to quantum Hamiltonian reductions. Finally, we study the def...
متن کاملFe b 20 09 Unitary representations of rational Cherednik
We study unitarity of lowest weight irreducible representations of rational Cherednik algebras. We prove several general results, and use them to determine which lowest weight representations are unitary in a number of cases. In particular, in type A, we give a full description of the unitarity locus (justified in Subsection 5.1 and the appendix written by S. Griffeth), and resolve a question b...
متن کامل