Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1)

Details Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1) Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1)

2005-12-13

arxiv.org/abs/math/0512257v4

Mathematics

Representation Theory

21pages

Scientific paper

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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