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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, October 12, 2017 - 3:00pm

Pasha Pylyavskyy

University of Minnesota


University of Pennsylvania


Kazhdan and Lusztig in their 1979 groundbreaking paper provided a new approach to representation theory of Hecke algebras of Coxeter groups. Their construction encodes the structure of a Hecke algebra representation by a directed weighted graph called W-graph. Stembridge undertook a deep study of those graphs and their certain connected components, called molecules. In type A those connected components turn out to be equivalent to dual equivalence graphs, which are certain graphs on standard Young tableaux. DEG-s have been actively used in the theory of symmetric functions in recent years. In this work we study the structure of Kazhdan-Lusztig molecules in affine type A, obtaining two affine analogs of dual equivalence graphs: one on affine permutations and one on tabloids.  We build on a previous work constructing an affine analog of Robinson-Schensted algorithm. This is a joint work with Michael Chmutov, Joel Lewis, and Elena Yudovina.