Restricted rational Cherednik algebras

Abstract

We give an overview of the representation theory of restricted rational Cherednik algebras. These are certain finite-dimensional quotients of rational Cherednik algebras at t=0. Their representation theory is connected to the geometry of the Calogero-Moser space, and there is a lot of evidence that they contain certain information about Hecke algebras even though the precise connection is so far unclear. We outline the basic theory along with some open problems and conjectures, and give explicit results in the cyclic and dihedral cases.

To appear in "Representation theory: Recent developments and perspectives from a priority programme"

References in corpus (8)

• Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras
• Finite dimensional quotients of Hecke algebras
• CHAMP: A Cherednik Algebra Magma Package
• Cellules de Calogero-Moser
• Cuspidal Calogero-Moser and Lusztig families for Coxeter groups
• Restricted rational Cherednik algebras
• Blocks in flat families of finite-dimensional algebras
• Blocks of restricted rational Cherednik algebras for $G(m,d,n)$

Cited by in corpus (5)

• CHAMP: A Cherednik Algebra Magma Package
• Cuspidal Calogero-Moser and Lusztig families for Coxeter groups
• Restricted rational Cherednik algebras
• Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution
• Wreath Macdonald polynomials at q=t as characters of rational Cherednik algebras