**SMS scnews item created by James East at Tue 9 Mar 2010 1031**

Type: Seminar

Modified: Tue 9 Mar 2010 1035

Distribution: World

Expiry: 12 Mar 2010

**Calendar1: 12 Mar 2010 1205-1255**

**CalLoc1: Carslaw 175**

Auth: jamese@bari.maths.usyd.edu.au

### Algebra Seminar

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

### Dan Nakano

#### Friday March 12, 12:05--12:55pm, Carslaw 175

###### Abstract

In 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.

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After the seminar we will take the speaker to lunch at Thai@Home, with the view to be back in time for Alex Dimca's Joint Colloquium talk (Carslaw 175, 2pm).

See the Algebra Seminar web page for information about other seminars in the series.

James East james.east@sydney.edu.au