Subspace Arrangements and Cherednik Algebras

On Cohomology Algebras of Complex Subspace Arrangements

The integer cohomology algebra of the complement of a complex subspace arrangement with geometric intersection lattice is completely determined by the combinatorial data of the arrangement. We give a combinatorial presentation of the cohomology algebra in the spirit of the Orlik-Solomon result on the cohomology algebras of complex hyperplane arrangements. Our methods are elementary: we work wit...

Cohomology Algebras of Complex Subspace Arrangements 3

Cherednik algebras and Yangians

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.

Rational 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.

Triple groups and Cherednik algebras

The goal of this paper is to define a new class of objects which we call triple groups and to relate them with Cherednik's double affine Heeke algebras. This has as immediate consequences new descriptions of double affine Weyl and Artin groups, the double affine Heeke algebras as well as the corresponding elliptic objects. From the new descriptions we recover results of Cherednik on automorphis...