Download or read book Cohomology for Quantum Groups via the Geometry of the Nullcone written by Christopher P. Bendel and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.