NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT

REPRESENTATION THEORY AND RELATED TOPICS SEMINAR



Arkady Berenstein

(University of Oregon)

Braided Doubles and Rational Cherednik Algebras

ABSTRACT:  In my talk (based on a recent joint paper with Yuri Bazlov) I will introduce a general class of algebras
with triangular decomposition which we call "braided doubles". Braided doubles provide a unifying framework for all classical and quantum universal enveloping algebras and recently discovered rational Cherednik algebras. 

Quite surprisingly, one can completely classify free braided doubles. The classification is achieved in terms of Yetter-Drinfeld (YD-)modules over Hopf algebras and their generalizations. In particular, to each R-matrix one associates a canonical YD-module so that the corresponding braided double U(R) is a  deformation of the Weyl algebra, where the role of polynomial algebras is played by Nichols-Woronowicz algebras. 

The main result is that any rational Cherednik algebra canonically embeds into the double U(R) attached to the
R-matrix emerging from each complex reflection group. This embedding gives a new definition of rational Cherednik algebras and the instantaneous proof of their triangular decomposition.

December 7, 2007
10:30 - 11:30
511 Lake Hall


For further information visit http://www.math.neu.edu/~martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky alexmart >at< neu >dot< edu