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.

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

References in corpus (2)

• Grothendieck polynomials and the Boson-Fermion correspondence
• Determinantal formulas for dual Grothendieck polynomials

Cited by in corpus (3)

• Free fermions and Schur expansions of multi-Schur functions
• Free fermionic probability theory and K-theoretic Schubert calculus
• Integrable models and $K$-theoretic pushforward of Grothendieck classes