Notes on Cherednik Algebras and Algebraic Combinatorics, Montreal 2017

Quivers of Type A, Flag Varieties and Representation Theory

Introduction. In this survey, we describe and relate various occurences of quivers of type A (both finite and affine) and their canonical bases in combinatorics, in algebraic geometry and in representation theory. The ubiquity of these quivers makes them especially important to study : they are pervasive in very classical topics (such as the theory of symmetric functions) as well as in some of ...

Cherednik and Hecke Algebras of Varieties with a Finite Group Action

Let h be a finite dimensional complex vector space, and G be a finite subgroup of GL(h). To this data one can attach a family of algebras Ht,c(h, G), called the rational Cherednik algebras (see [EG]); for t = 1 it provides the universal deformation of G ⋉ D(h) (where D(h) is the algebra of differential operators on h). These algebras are generated by G, h, h with certain commutation relations, ...

Parabolic 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...

Lecture Notes on Cherednik Algebras

Cylindrical Combinatorics and Representations of Cherednik Algebras of Type A

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...