Compound basis arising from the basic $A^{(1)}_{1}$-module

TL;DR

This paper introduces a novel basis for an infinite-variable polynomial ring, combining Schur functions and Q-functions, and studies the transition matrix from the standard Schur basis.

Contribution

It constructs a new basis involving Schur and Q-functions and analyzes the transition matrix from the classical Schur basis.

Findings

New basis combining Schur and Q-functions

Transition matrix from Schur basis characterized

Potential applications in representation theory

Abstract

A new basis for the polynomial ring of infinitely many variables is constructed which consists of products of Schur functions and Q-functions. The transition matrix from the natural Schur function basis is investigated.