COSETS FROM EQUIVARIANT W-ALGEBRAS

Creutzig T, Nakatsuka S (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Representation Theory American Mathematical Society

Book Volume: 27

Pages Range: 766-777

DOI: 10.1090/ert/651

Abstract

The equivariant W-algebra of a simple Lie algebra g is a BRST reduction of the algebra of chiral differential operators on the Lie group of g. We construct a family of vertex algebras A[g, k, n] as subalgebras of the equivariant W-algebra of g tensored with the integrable affine vertex algebra Ln(ǧ) of the Langlands dual Lie algebra ǧ at level n ∈ Z>0. They are conformal extensions of the tensor product of an affine vertex algebra and the principal W-algebra whose levels satisfy a specific relation. When g is of type ADE, we identify A[g, k, 1] with the affine vertex algebra V^k−1(g) ⊗ L1(g), giving a new and efficient proof of the coset realization of the principal W-algebras of type ADE.

Involved external institutions

University of Alberta

Canada (CA)

How to cite

APA:

Creutzig, T., & Nakatsuka, S. (2023). COSETS FROM EQUIVARIANT W-ALGEBRAS. Representation Theory, 27, 766-777. https://doi.org/10.1090/ert/651

MLA:

Creutzig, Thomas, and Shigenori Nakatsuka. "COSETS FROM EQUIVARIANT W-ALGEBRAS." Representation Theory 27 (2023): 766-777.

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