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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
*F*_{w}^{C}(**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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