Bilinear expansion of Schur functions in Schur $Q$-functions: a fermionic approach

TL;DR

This paper derives a new identity expressing Schur functions as sums over products of Schur $Q$-functions using a fermionic approach, expanding the mathematical understanding of symmetric functions.

Contribution

It introduces a novel fermionic representation-based identity that generalizes previous special cases of Schur and Schur $Q$-functions relations.

Findings

Derived a new identity linking Schur and Schur $Q$-functions.

Utilized fermionic creation and annihilation operators in the derivation.

Applied Wick's theorem and factorization of vacuum expectation values.

Abstract

An identity is derived expressing Schur functions as sums over products of pairs of Schur $Q$-functions, generalizing previously known special cases. This is shown to follow from their representations as vacuum expectation values (VEV's) of products of either charged or neutral fermionic creation and annihilation operators, Wick's theorem and a factorization identity for VEV's of products of two mutually anticommuting sets of neutral fermionic operators.