The Jacobian, Reflection Arrangement and Discriminant for Reflection Hopf Algebras

Reflection Functors and Symplectic Reflection Algebras for Wreath Products

We construct reflection functors on categories of modules over deformed wreath products of the preprojective algebra of a quiver. These functors give equivalences of categories associated to generic parameters which are in the same orbit under the Weyl group action. We give applications to the representation theory of symplectic reflection algebras of wreath product groups.

Symplectic Reflection Algebras

Continuous symplectic reflection algebras

The theory of PBW properties of quadratic algebras, to which this paper aims to be a modest contribution, originates from the pioneering work of Drinfeld (see [Dr1]). In particular, as we learned after publication of [EG] (to the embarrassment of two of us!), symplectic reflection algebras and even more general reflection algebras considered in Section 3.6 below, as well as PBW theorems for the...

Symplectic Reflection Algebras

We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, with category O, and with spaces of representations of quivers. Mathematics Subject Classification (2000). Primary 16G.

Representations of reflection algebras

We study a class of algebras B(n, l) associated with integrable models with boundaries. These algebras can be identified with coideal subalgebras in the Yangian for gl(n). We construct an analog of the quantum determinant and show that its coefficients generate the center of B(n, l). We develop an analog of Drinfeld’s highest weight theory for these algebras and give a complete description of t...