Séminaire Lotharingien de Combinatoire, 78B.8 (2017), 10 pp.

Graham Hawkes, Kirill Paramonov and Anne Schilling

Crystal Analysis of Type C Stanley Symmetric Functions

Abstract. Combining results of T. K. Lam and J. Stembridge, the type C Stanley symmetric function FwC(x), indexed by an element w in the type C Coxeter group, has a nonnegative integer expansion in terms of Schur functions. We provide a crystal theoretic explanation of this fact and give an explicit combinatorial description of the coefficients in the Schur expansion in terms of highest weight crystal elements.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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