Positive specializations of K-theoretic Schur P- and Q-functions

TL;DR

This paper classifies positive specializations of K-theoretic Schur P- and Q-functions, extending classical theorems and exploring their applications to harmonic functions on shifted Young lattices.

Contribution

It extends the classification of positive specializations to shifted K-theoretic Schur functions, building on Nazarov's shifted Edrei-Thoma theorem.

Findings

Extended shifted Edrei-Thoma theorem for K-theoretic Schur P- and Q-functions.

Provided a classification of positive specializations for these functions.

Discussed applications to extreme harmonic functions on shifted Young lattices.

Abstract

Yeliussizov has classified the positive specializations of symmetric Grothendieck functions, defined in several different ways, providing a K-theoretic lift of the classical Edrei-Thoma theorem. This note studies the analogous classification problem for Ikeda and Naruse's K-theoretic Schur P- and Q-functions, which are the shifted versions of symmetric Grothendieck functions. Our results extend a shifted variant of the Edrei-Thoma theorem due to Nazarov. We also discuss an application to the problem of determining the extreme harmonic functions on a filtered version of the shifted Young lattice.