Rectangular Schur functions and the basic representation of affine Lie algebras
classification
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affinebasicrectangularrepresentationschursquarealgebraalgebras
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An expression is given for the plethysm $p_{2}\circ S_{\square}$, where $p_{2}$ is the power sum of degree two and $S_{\square}$ is the Schur function indexed by a rectangular partition. The formula can be well understood from the viewpoint of the basic representation of the affine Lie algebra of type $A_{2}^{(2)}$.
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