Takeshi Ikeda, Hiroshi Mizukawa, Tatsuhiro Nakajima, Hiro-Fumi Yamada
Published 2005-12-13, updated 2007-04-10Version 4
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 A_1^{(1)}. A realization of the basic representation that is of ``D_2^{(2)}''-type plays the central role.
On $q$-series for principal characters of standard $A_2^{(2)}$-modules
A non-recursive criterion for weights of a highest weight module for an affine Lie algebra
New Irreducible Modules for Heisenberg and Affine Lie Algebras
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