Several USC School of Architecture Faculty Members to have featured work in Exhibit at the Museum of Contemporary Art
June 16-September 16
Discover art spanning five centuries at USC Fisher Museum of Art.
Quantum Schubert cells via representation and ring theory
Monday, November 19, 2012 : 3:30pm to 4:30pm
University Park Campus
Joel Geiger, Louisiana State University,
The quantum Schubert cell algebras defined by De Concini, Kac, and Procesi and independently by Lusztig comprise a large and versatile collection of subalgebras of the positive part of the quantized universal enveloping algebras. In this talk I will outline two major approaches to understanding the noncommutative prime spectra of the quantum Schubert cell algebras --- a ring theoretic approach due to Gerard Cauchon and a representation theoretic approach due to Milen Yakimov. We answer a question of Cauchon and M'erieaux, thereby unifying the two seemingly disparate approaches. Time permitting we will also investigate a result relating this unified approach to the theory of quantum cluster algebras. This work is joint with Milen Yakimov.