Intermediate symplectic $Q$-functions

TL;DR

This paper introduces a new family of Laurent polynomials called intermediate symplectic Q-functions, bridging existing symmetric functions and characters, with explicit formulas for their computation.

Contribution

It defines the intermediate symplectic Q-functions, providing tableau-sum and Pfaffian formulas, expanding the theory of symmetric functions and their representations.

Findings

Defined the intermediate symplectic Q-functions

Derived tableau-sum formula for these functions

Established Pfaffian formula for computational purposes

Abstract

We introduce an intermediate family of Laurent polynomials between Schur's $Q$-functions and S. Okada's symplectic $Q$-functions. It can also be regarded as a $Q$-function analogue of Proctor's intermediate symplectic characters, and is named the family of intermediate symplectic $Q$-functions. We also derive a tableau-sum formula and a J\'ozefiak-Pragacz-type Pfaffian formula of the Laurent polynomials.