New Schur function series

Masao Ishikawa, Masato Wakayama

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2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)480-525
Number of pages46
JournalJournal of Algebra
Volume208
Issue number2
DOIs
Publication statusPublished - Oct 15 1998

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Ishikawa, M., & Wakayama, M. (1998). New Schur function series. Journal of Algebra, 208(2), 480-525. https://doi.org/10.1006/jabr.1998.7509