Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1)
Representation Theory
2007-05-23 v4 Combinatorics
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 A_1^{(1)}. A realization of the basic representation that is of ``D_2^{(2)}''-type plays the central role.
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Cite
@article{arxiv.math/0512257,
title = {Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1)},
author = {Takeshi Ikeda and Hiroshi Mizukawa and Tatsuhiro Nakajima and Hiro-Fumi Yamada},
journal= {arXiv preprint arXiv:math/0512257},
year = {2007}
}
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21pages