Virasoro Action on the $Q$-Functions

TL;DR

This paper presents a formula describing how Virasoro operators act on Schur Q-functions, providing explicit results for strict partitions and the operators' effects.

Contribution

It introduces a new formula for the Virasoro action on Schur Q-functions, including explicit expressions for strict partitions.

Findings

Derived a formula for Virasoro operators acting on Schur Q-functions

Provided explicit expressions for the action on strict partitions

Enhanced understanding of Virasoro symmetry in symmetric functions

Abstract

A formula for Schur $Q$-functions is presented which describes the action of the Virasoro operators. For a strict partition, we prove a concise formula for $L_{-k}Q_{\lambda}$, where $L_{-k}$ $(k\geq 1)$ is the Virasoro operator.