Pfaffian Formulas and Schur Q-Function Identities

Abstract

We establish Pfaffian analogues of the Cauchy--Binet formula and the Ishikawa--Wakayama minor-summation formula. Each of these Pfaffian analogues expresses a sum of products of subpfaffians of two skew-symmetric matrices in terms of a single Pfaffian. By using these Pfaffian formulas we give new transparent proofs to several identities for Schur Q23 pa-functions.

23 pages

References in corpus (2)

• Interpolation analogues of Schur Q-functions
• A Generalization of Schur's $P$- and $Q$-Functions

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