Monday, April 3, 2017 at 3:00 PM in SAS 4201
Max Glick, University of Connecticut
The Berenstein-Kirillov group and cactus groups
Berenstein and Kirillov have studied the action of Bender-Knuth moves on semistandard tableaux. Losev has studied a cactus group action in Kazhdan-Lusztig theory; in type A this action can also be identified in the work of Henriques and Kamnitzer. We establish the relationship between the two actions. We show that the Berenstein-Kirillov group is a quotient of the cactus group. We use this to derive previously unknown relations in the Berenstein-Kirillov group. This is joint work with M. Chmutov and P. Pylyavskyy.
Friday, April 21, 2017 at 3:00 PM in SAS 1102
Mark Shimozono, Virginia Tech
Quiver Hall-Littlewood symmetric functions and Kostka-Shoji polynomials
We associate to any quiver a family of symmetric functions, defined by creation operators which are generalizations of Jing's creation operators. For the cyclic quiver the coefficient polynomials were studied by Finkelberg and Ionov. Shoji has recently shown that the single variable specialization of the Finkelberg-Ionov polynomials agree with polynomials he studied in relation to Green functions for reflection groups. For the cyclic quiver we give an explicit conjecture for the Finkelberg-Ionov polynomials involving multitableaux and charge. We conjecture Schur positivity for any quiver. This is joint work with Dan Orr.
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