BILINEAR EXPANSION OF SCHUR FUNCTIONS IN SCHUR Q-FUNCTIONS: A FERMIONIC APPROACH

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.

Automated summary

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