Rational Cherednik algebras
نویسنده
چکیده
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.
منابع مشابه
Applications 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 کاملEndomorphisms of Verma Modules for Rational Cherednik Algebras
We study the endomorphism algebras of Verma modules for rational Cherednik algebras at t = 0. It is shown that, in many cases, these endomorphism algebras are quotients of the centre of the rational Cherednik algebra. Geometrically, they define Lagrangian subvarieties of the generalized Calogero–Moser space. In the introduction, we motivate our results by describing them in the context of deriv...
متن کاملBaby Verma Modules for Rational Cherednik Algebras
These are notes for a talk in the MIT-Northeastern Spring 2015 Geometric Representation Theory Seminar. The main source is [G02]. We discuss baby Verma modules for rational Cherednik algebras at t = 0.
متن کاملCuspidal 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 کاملParabolic Degeneration of Rational Cherednik Algebras
We introduce parabolic degenerations of rational Cherednik algebras of complex reflection groups, and use them to give necessary conditions for finite-dimensionality of an irreducible lowest weight module for the rational Cherednik algebra of a complex reflection group, and for the existence of a non-zero map between two standard modules. The latter condition reproduces and enhances, in the cas...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010