Cuspidal representations of rational Cherednik algebras at t = 0
نویسندگان
چکیده
منابع مشابه
Cuspidal Representations of Rational Cherednik Algebras
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 .
متن کاملUnitary 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 کاملRational Cherednik algebras
We survey a number of results about rational Cherednik algebra representation theory and its connection to symplectic singularities and their resolutions. Mathematics Subject Classification (2000). Primary 16G, 17B; Secondary 20C, 53D.
متن کاملThe Dunkl Weight Function for Representations of Rational Cherednik Algebras
1. Signature Characters and the Jantzen Filtration 1 1.1. Jantzen Filtrations on Standard Modules 1 1.2. Hermitian Duals 3 1.3. Rationality of Signature Characters 5 1.4. Asymptotic Signatures 7 1.5. Isotypic Signature Characters 8 2. The Dunkl Weight Function 10 2.1. The Gaussian Inner Product 10 2.2. Weight Function 10 2.3. Analytic Continuation on the Regular Locus 20 2.4. Extension to Distr...
متن کاملRational Cherednik Algebras and Hilbert Schemes Ii: Representations and Sheaves
Let Hc be the rational Cherednik algebra of type An−1 with spherical subalgebra Uc = eHce. Then Uc is filtered by order of differential operators with associated graded ring grUc = C[h ⊕ h∗]W , where W is the n-th symmetric group. Using the Z-algebra construction from [GS] it is also possible to associate to a filtered Hcor Uc-module M a coherent sheaf Φ̂(M) on the Hilbert scheme Hilb(n). Using ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2010
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-010-0754-x