Algebraic formulas for the structure constants in symmetric functions

TL;DR

This paper derives algebraic formulas for the structure constants in symmetric functions, extending combinatorial decomposition rules through vertex operator realizations.

Contribution

It introduces algebraic forms of decomposition formulas for symmetric functions using vertex operator methods, advancing beyond combinatorial approaches.

Findings

Algebraic formulas for structure constants are constructed.

Vertex operator realizations provide new algebraic insights.

Extends decomposition formulas to Hall-Littlewood functions and universal characters.

Abstract

Littlewood-Richardson rule gives the decomposition formula for the multiplication of two Schur functions, while the decomposition formula for the multiplication of two Hall-Littlewood functions or two universal characters is also given by the combinatorial method. In this paper, using the vertex operator realizations of these symmetric functions, we construct the algebraic forms of these decomposition formulas.