Applications of minor-summation formula. II: Pfaffians and Schur polynomials
[For part I see the authors and \textit{S. Okada}, J. Algebras 183, No. 1, 193-216 (1996; Zbl 0857.15005).] In the present part II minor-summation formulas of Pfaffians are derived using new generating functions involving Schur polynomials with two parameters, which have a product representation. The prototype of these formulas is the Littlewood formula [cf. \textit{D. E. Littlewood}, Symmetric functions and Hall polynomials, Second edition, Oxford Univ. Press, Oxford (1950)]. Applying the minor-summation formula developed by the authors [Linear Multilinear Algebra 39, No. 3, 285-305 (1995; Zbl 0830.15011)] the Littlewood formulas may be extended in various directions. The formulas are proved algebraically by evaluating certain Pfaffians and by developing some techniques to compute sub-Pfaffians of a given skew-symmetric matrix.
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