On the structure of W-algebras in type A

Creutzig T, Fasquel J, Linshaw AR, Nakatsuka S (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Japanese Journal of Mathematics Springer Verlag (Germany)

Book Volume: 20

Pages Range: 1-111

Journal Issue: 1

DOI: 10.1007/s11537-025-2414-2

Abstract

We formulate and prove examples of a conjecture which describes the W−algebras in type A as successive quantum Hamiltonian reductions of affine vertex algebras associated with several hook-type nilpotent orbits. This implies that the affine coset subalgebras of hook-type W−algebras are building blocks of the W−algebras in type A. In the rational case, it turns out that the building blocks for the simple quotients are provided by the minimal series of the regular W−algebras. In contrast, they are provided by singlet-type extensions of W−algebras at collapsing levels which are irrational. In the latter case, several new sporadic isomorphisms between different W−algebras are established.

Authors with CRIS profile

Thomas Creutzig Lehrstuhl für Darstellungstheorie Shigenori Nakatsuka Lehrstuhl für Darstellungstheorie

Involved external institutions

The University of Melbourne AU Australia (AU) University of Denver US United States (USA) (US)

How to cite

APA:

Creutzig, T., Fasquel, J., Linshaw, A.R., & Nakatsuka, S. (2025). On the structure of W-algebras in type A. Japanese Journal of Mathematics, 20(1), 1-111. https://doi.org/10.1007/s11537-025-2414-2

MLA:

Creutzig, Thomas, et al. "On the structure of W-algebras in type A." Japanese Journal of Mathematics 20.1 (2025): 1-111.

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