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

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

doi:10.1016/j.aam.2007.05.003

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

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	514-535
Number of pages	22
Journal	Advances in Applied Mathematics
Volume	40
Issue number	4
DOIs	https://doi.org/10.1016/j.aam.2007.05.003
Publication status	Published - 2008 May
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1016/j.aam.2007.05.003

Cite this

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AU - Ikeda, Takeshi

AU - Mizukawa, Hiroshi

AU - Nakajima, Tatsuhiro

AU - Yamada, Hiro Fumi

PY - 2008/5

Y1 - 2008/5

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KW - Boson-fermion correspondence

KW - Schur function

KW - Schur's Q-function

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