Kazuya Aokage, Eriko Shinkawa, Hiro-Fumi Yamada, “Virasoro Action on the <nobr>$Q$</nobr>-Functions”, SIGMA, 2021, Volume 17,089, 12 pp.

Virasoro Action on the $Q$-Functions

Kazuya Aokage^a, Eriko Shinkawa^b, Hiro-Fumi Yamada^c

^a Department of Mathematics, National Institute of Technology, Ariake College, Fukuoka 836-8585, Japan
^b Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
^c Department of Mathematics, Kumamoto University, Kumamoto 860-8555, Japan

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.

Keywords: $Q$-functions, Virasoro operators.

MSC: 17B68, 05E10

Received: June 10, 2021; in final form October 5, 2021; Published online October 8, 2021

Language: English

DOI: 10.3842/SIGMA.2021.089