Rectangular Schur functions and the basic representation of affine Lie algebras

Abstract

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 $A_2^{(2)}$.

16 pages