Pfaffian Formulas and Schur Q-Function Identities

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.