✦ LIBER ✦

New Schur Function Series

✍ Scribed by Masao Ishikawa; Masato Wakayama

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 445 KB
Volume: 208
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7509

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✦ Synopsis

This paper presents some new product identities for certain summations of Schur functions. These identities are generalizations of some famous identities known to Littlewood and appearing in Macdonald's book. We refer to these identities as the ''Littlewood-type formulas.'' In addition, analogues for summations of characters of the other classical groups are also given. The Littlewood-type formulas in this paper are separated into two classes, the rational Schur function series and the generalized Schur function series. An application of a rational Schur function series to the infinite product representation of the elliptic theta functions is also given. We prove these Littlewood-type formulas using the Cauchy᎐Binet formula. The Cauchy᎐Binet formula is a basic but powerful tool applicable in the present context, which can be derived from our Pfaffian formula, as we explain.

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