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arXiv · 1305.1394

Schur function identities arising from the basic representation of $A^{(2)}_{2}$

Hiroshi Mizukawa·Tatsuhiro Nakajima·Ryoji Seno·Hiro-Fumi Yamada
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Abstract

A Lie theoretic interpretation is given for some formulas of Schur functions and Schur $Q$-functions. Two realizations of the basic representation of the Lie algebra $A^{(2)}_2$ are considered; one is on the fermionic Fock space and the other is on the bosonic polynomial space. Via the boson-fermion correspondence, simple relations of the vacuum expectation values of fermions turn out to be algebraic relations of Schur functions.

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Hiroshi Mizukawa, Tatsuhiro Nakajima, Ryoji Seno, Hiro-Fumi Yamada. 2013-08-30. Schur function identities arising from the basic representation of $A^{(2)}_{2}$. https://doi.org/10.1007/s11005-014-0717-y

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