Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A1(1)

Takeshi Ikeda, Hiroshi Mizukawa, Tatsuhiro Nakajima, Hiro Fumi Yamada

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Formulas are obtained that express the Schur S-functions indexed by Young diagrams of rectangular shape as linear combinations of "mixed" products of Schur's S- and Q-functions. The proof is achieved by using representations of the affine Lie algebra of type A1(1). A realization of the basic representation that is of "D2(2)"-type plays the central role.

Original languageEnglish
Pages (from-to)514-535
Number of pages22
JournalAdvances in Applied Mathematics
Volume40
Issue number4
DOIs
Publication statusPublished - May 2008

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Young Diagram
Affine Lie Algebras
Q-function
Schur Functions
Algebra
Linear Combination
Express

Keywords

  • Boson-fermion correspondence
  • Schur function
  • Schur's Q-function

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A1(1). / Ikeda, Takeshi; Mizukawa, Hiroshi; Nakajima, Tatsuhiro; Yamada, Hiro Fumi.

In: Advances in Applied Mathematics, Vol. 40, No. 4, 05.2008, p. 514-535.

Research output: Contribution to journalArticle

Ikeda, Takeshi ; Mizukawa, Hiroshi ; Nakajima, Tatsuhiro ; Yamada, Hiro Fumi. / Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A1(1). In: Advances in Applied Mathematics. 2008 ; Vol. 40, No. 4. pp. 514-535.
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