Speaker: Justin Lambright, Lehigh University
Title: A combinatorial interpretation for computations in the quantum polynomial ring.
Time: 2:30 PM, Monday, November 16, 2009
Place: Malott 206
Abstract: A Hopf algebra called the quantum coordinate ring of SL(n,C) is often
studied in terms of a related noncommutative ring called the quantum polynomial
ring in n2 variables. Various bases of these rings and their
representation-theoretic applications lead to the study of transition matrices
whose entries are commutative polynomials having nonnegative integer
coefficients. Examples of such polynomials include Brenti's modified
R-polynomials. We generalize Brenti's work to give combinatorial
interpretations for coefficients in a larger class of transition matrices. As
an application, we simplify somewhat the previous formulation of the dual
canonical basis of the quantum polynomial ring.
October 22, 2009