Set-valued domino tableaux and shifted set-valued domino tableaux

TL;DR

This paper extends classical combinatorial bijections to the K-theoretic setting, providing new product formulas for Grothendieck and Q-Schur functions using domino tableaux.

Contribution

It introduces set-valued and shifted set-valued domino tableaux and establishes their connection to K-theoretic symmetric functions, advancing combinatorial representation theory.

Findings

Established K-theoretic bijections for domino tableaux

Derived product formulas for stable Grothendieck polynomials

Extended combinatorial models to shifted set-valued tableaux

Abstract

We prove K-theoretic and shifted K-theoretic analogues of the bijection of Stanton and White between domino tableaux and pairs of semistandard tableaux. As a result, we obtain product formulas for pairs of stable Grothendieck polynomials and pairs of K-theoretic Q-Schur functions.