Abstract The purpose of this article is to study the relationship between numerical invariants certain subspace arrangements coming from reflection groups and arising in representation theory Cherednik algebras. For instance, we observe that knowledge equivariant graded Betti numbers (in sense commutative algebra) any irreducible category ${\mathscr{O}}$ equivalent Kazhdan–Lusztig character obj...

We investigate the representation theory of the rational and trigonometric Cherednik algebra of type GLn by means of combinatorics on periodic (or cylindrical) skew diagrams. We introduce and study standard tableaux and plane partitions on periodic diagrams, and in particular, compute some generating functions concerning plane partitions, where Kostka polynomials and their level restricted gene...

Introduction. Jack's and Macdonald's polynomials are an important class of symmetric functions associated to root systems. In this paper we deene and study an analogue of Jack's and Macdonald's polynomials for aane root systems. Our approach is based on representation theory of aane Lie algebras and quantum aane algebras, and follows the ideas of our recent papers EK1,EK2,EK3]. We start with a ...

We identify the Bethe algebra of the Gaudin model associated to gl N acting on a suitable representation with the center of the rational Cherednik algebra and with the algebra of regular functions on the Calogero-Moser space.

We give a detailed account of a combinatorial construction, due to Cherednik, of cyclic generators for irreducible modules of the affine Hecke algebra of the general linear group with generic parameter q.

We construct a functor from the category of modules over the trigonometric (resp. rational) Cherednik algebra of type gll to the category of integrable modules of level l over a Yangian for the loop algebra sln (resp. over a subalgebra of this Yangian called the Yangian deformed double loop algebra) and we establish that it is an equivalence of categories if l + 2 < n.

In this paper we determine the support of the irreducible spherical representation (i.e., the irreducible quotient of the polynomial representation) of the rational Cherednik algebra of a finite Coxeter group for any value of the parameter c. In particular, we determine for which values of c this representation is finite dimensional. This generalizes a result of Varagnolo and Vasserot, [VV], wh...