Cohomology for Quantum Groups via the Geometry of the Nullcone

In general, little is known about the representation theory of quantum groups (resp., algebraic groups) when l (resp., p ) is smaller than the Coxeter number h of the underlying root system. For example, Lusztig's conjecture concerning the characters of the rational irreducible G -modules stipulates that p=h. The main result in this paper provides a surprisingly uniform answer for the cohomology algebra H (u ? ,C) of the small quantum group.

• Author: Christopher P. Bendel, Daniel K. Nakano, Brian J. Parshal, Cornelius Pillen
• Publisher: American Mathematical Soc.
• Published: 2014-04-07
• Pages: 110