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Schur Function Identities Arising From the Basic Representation of {A^{(2)}_{2}} |
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| Authors: | Hiroshi Mizukawa Tatsuhiro Nakajima Ryoji Seno Hiro-Fumi Yamada |
| Affiliation: | 1. Department of Mathematics, National Defense Academy of Japan, Yokosuka, 239-8686, Japan 2. Faculty of Economics, Meikai University, Urayasu, 279-8550, Japan 3. NEC System Technologies, Ltd., Osaka, Japan 4. Department of Mathematics, Okayama University, Okayama, 700-8530, Japan |
| 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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