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Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra |
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| Authors: | Takeshi Ikeda Hiroshi Mizukawa Tatsuhiro Nakajima Hiro-Fumi Yamada |
| Institution: | aDepartment of Applied Mathematics, Okayama University of Science, Okayama 700-0005, Japan;bDepartment of Mathematics, National Defense Academy, Yokosuka 239-8686, Japan;cFaculty of Economics, Meikai University, Urayasu 279-8550, Japan;dDepartment of Mathematics, Okayama University, Okayama 700-8530, Japan |
| 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 |
| Keywords: | Schur function Schur's Q-function Boson– fermion correspondence |
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