Séminaire Lotharingien de Combinatoire, 82B.27 (2019), 12 pp.

Cara Monical, Oliver Pechenik, and Travis Scrimshaw

Crystal structures for symmetric Grothendieck polynomials

Abstract. We construct a type A_n crystal structure on semistandard set-valued tableaux, which yields a new formula and proof for the Schur positivity of symmetric Grothendieck polynomials. For single rows and columns, we construct a K-theoretic analog of crystals and new interpretation of Lascoux polynomials. We relate our crystal structures to the 5-vertex model using Gelfand-Tsetlin patterns.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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