Algebra and Discrete Mathematics Seminar, UC Davis

Stephen Griffeth, Universidad de Talca

Special parameters for rational Cherednik algebras

Organizer's time: 2021-01-21 09:30 America/Los_Angeles

Duration: 1 hour

The rational Cherednik algebra associated with a complex reflection group W is a certain deformation of an algebra of differential operators, with deformation parameter "c" running over a vector space of dimension equal to the number of conjugacy classes of reflections in W. Given a yes or no question about the structure of the Cherednik algebra produces a subset of the parameter space consisting of those c for which the answer is "yes." I will discuss a number of such questions, such as "Does there exist a non-trivial ideal in the Cherednik algebra?", "Is the top of the polynomial representation finite dimensional?" and "Is the Cherednik algebra Morita equivalent to its spherical subalgebra?" In those cases for which explicit descriptions of the corresponding set of c are available I will discuss some of the techniques used to obtain them, and survey some of the most important unresolved questions. This talk is partly based on joint work with Charles Dunkl, Susanna Fishel, Daniel Juteau, and Elizabeth Manosalva.

Submitted by: Eugene Gorsky