Classification of irreducible Harish-Chandra modules over full toroidal Lie algebras and higher-dimensional Virasoro algebras

Title

Classification of irreducible Harish-Chandra modules over full toroidal Lie algebras and higher-dimensional Virasoro algebras

Creator

Pal, Souvik

Description

In this paper, we classify the irreducible Harish-Chandra modules over the full toroidal Lie algebra, which is a natural higherdimensional analogue of the affine-Virasoro algebra. In particular, we complete the classification of irreducible bounded modules studied by Billig for non-zero level modules [Int. Math. Res. Not. 2006]. As a by-product, we also obtain the classification of irreducible Harish-Chandra modules over the higher-dimensional Virasoro algebra, which was introduced by RaoMoody [Comm. Math. Phys. 1994], thereby generalizing the well-known result of O. Mathieu [Invent. Math. 1992] for the classical Virasoro algebra. More precisely, we show that any irreducible Harish-Chandra module over the higher-dimensional Virasoro algebra turns out to be either a quotient of a module of tensor fields on a torus or a highest weight type module up to a twist of an automorphism, as conjectured by Eswara Rao in 2004. 2025, International Press, Inc. All rights reserved.

Source

Mathematical Research Letters;Volume;32;Issue;4;pp.1197-1248

Date

01-01-2025

Publisher

International Press, Inc.

Coverage

Pal S., Department of Mathematics, Indian Institute of Science, Karnataka, Bengaluru, 560012, India, Department of Sciences and Humanities, CHRIST University, Bengaluru, 560 074, India

Rights

All Open Access; Green Open Access

Relation

ISSN: 10732780;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.4310/MRL.251124182522

https://www.scopus.com/pages/publications/105032239576?origin=resultslist