# Differentiating the Weyl generic dimension formula and support varieties for quantum groups

Algebra/Geometry/Topology Seminar

#### by Dan Nakano

Institution: University of Georgia
Date: Thu 15th April 2010
Time: 2:15 PM
Location: Babel Middle Theatrette (106)

Abstract: n this talk I will explain how to compute the support varieties of all the irreducible modules for the small quantum group u_{zeta}(g) where g is a simple, complex Lie algebra and zeta is an l-th root of unity larger than the Coxeter number. This calculation employs the prior calculations and techniques of Ostrik and of Nakano--Parshall--Vella, in addition to deep results involving the validity of the Lusztig character formula and the positivity of parabolic Kazhdan-Lusztig polynomials for the affine Weyl group. Analogous results are provided for the first Frobenius kernel G_1 of a reductive algebraic group scheme G defined over the prime field F_p. This is joint work with C. Drupieski and B. Parshall.