Crystal structures for symmetric Grothendieck polynomials. (English) Zbl 1436.05131
Summary: 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.
MSC:
| 05E10 | Combinatorial aspects of representation theory |
| 14N15 | Classical problems, Schubert calculus |
Software:
SageMathReferences:
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