Free-fermions and skew stable Grothendieck polynomials

Abstract

Skew stable Grothendieck polynomials are $K$-theoretic analogues of skew Schur polynomials. We give a free-fermionic presentation of skew stable Grothendieck polynomials and their dual symmetric functions. By using our presentation, we derive a family of determinantal formulas, which are $K$-analogues of the Jacobi-Trudi formula for skew Schur functions. We also introduce a combinatorial method to calculate certain expansions of skew (dual) stable Grothendieck polynomials by using the non-commutative supersymmetric Schur functions.

arXiv comment25 pages. This work is a continuation of the author's previous work arXiv:1905.07692

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• Free fermionic probability theory and K-theoretic Schubert calculus
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