Sergeev's formula and the littlewood—richardson rule

Abstract

We give here a direct and elementary proof of a two variable extension of the classical bideterminantal formula of Jacobi for Schur functions. This formula, due to A. Sergeev, is a new expression for the Schur function Sλ(X — Y) (λ-ring notation). We also show that this formula is intimately related to the Littlewood-Richardson rule. More precisely we show that one can be derived from the other by a very simple tableau involution. Consequently, our derivation of the Sergeev formula provides what may be the most direct and simple path to the famed Littlewood-Richardson result.

^*Work of both authors was supported by NSF grant at the University of California at San Diego.

^*Work of both authors was supported by NSF grant at the University of California at San Diego.

Notes

^*Work of both authors was supported by NSF grant at the University of California at San Diego.