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Bilinear expansion of Schur functions in Schur $Q$-functions: a fermionic approach (2008.13734v5)
Published 31 Aug 2020 in math-ph, math.CO, math.GR, math.MP, math.RA, and nlin.SI
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.