Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 089, 12 pages      arXiv:2106.04773

Virasoro Action on the $Q$-Functions

Kazuya Aokage a, Eriko Shinkawa b and 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

Received June 10, 2021, in final form October 05, 2021; Published online October 08, 2021

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.

Key words: $Q$-functions; Virasoro operators.

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