Special values of $K$-theoretic Schur $P$- and $Q$-functions

TL;DR

This paper determines special values of $K$-theoretic Schur $P$- and $Q$-functions, revealing combinatorial properties and generalizations related to shifted set-valued skew tableaux.

Contribution

It provides explicit special values for skew $K$-theoretic Schur functions and explores their combinatorial implications and generalizations.

Findings

Established special values for skew $K$-theoretic Schur functions

Proved an oddness property of shifted set-valued skew tableaux

Generalized special values to other skew cases

Abstract

We provide the special values of the skew version of the $K$-theoretic Schur $P$- and $Q$-functions. Using these special values, we show an oddness property of the number of shifted set-valued skew tableaux. Additionally, we generalize these special values to another skew case. Based on these special values, we give pairs among certain shifted set-valued skew tableaux.