The classical Littlewood-Richardson coefficients areremarkable nonnegative integers which occupy aprominent place in combinatorics, representation theoryand geometry. We review some versions of the originalrule for their calculation then follow by a naturalgeneralization of these coefficients called the Littlewood-Richardson polynomials and give a combinatorial rulefor their calculation. This rule is applied to find theproduct of the Casimir elements for the general linearLie algebra in the basis of the quantum immanantsconstructed by A. Okounkov and G. Olshanski. The samerule yields a positive and stable formula for the productof equivariant Schubert classes on the Grassmannian andit is equivalent to the positive formula for such a productfirst given by A. Knutson and T. Tao by usingcombinatorics of puzzles.

Alexander Molev, December 6, 2010

Partially supported by NSF.

Alexander MolevUniversity of Sydney

Will present the FortiethWilliam J. Spencer Lecture

Title of Talk:

“Littlewood-Richardson Polynomials”

Thursday, February 10, 20112:30 PM

102 Cardwell HallKansas State University

Manhattan, Kansas

All are invited