A commutant realization of Odake's algebra

Creutzig T, Linshaw AR (2013)

Publication Type: Journal article

Publication year: 2013

Journal

Transformation Groups Springer Verlag (Germany)

Book Volume: 18

Pages Range: 615-637

Journal Issue: 3

DOI: 10.1007/s00031-013-9235-8

Abstract

The bcβγ-system W of rank 3 has an action of the affine vertex algebra V0(sl2), and the commutant vertex algebra C = Com(V0(sl2),W) contains copies of V-3/2(sl2) and Odake's algebra O. Odake's algebra is an extension of the N = 2 super-conformal algebra with c = 9, and is generated by eight fields which close nonlinearly under operator product expansions. Our main result is that V-3/2(sl2) and O form a Howe pair (i.e., a pair of mutual commutants) inside C. More generally, any finite-dimensional representation of a Lie algebra g gives rise to a similar Howe pair, and this example corresponds to the adjoint representation of sl2. © 2013 Springer Science+Business Media New York.

Involved external institutions

University of Alberta CA Canada (CA) University of Denver US United States (USA) (US)

How to cite

APA:

Creutzig, T., & Linshaw, A.R. (2013). A commutant realization of Odake's algebra. Transformation Groups, 18(3), 615-637. https://doi.org/10.1007/s00031-013-9235-8

MLA:

Creutzig, Thomas, and Andrew R. Linshaw. "A commutant realization of Odake's algebra." Transformation Groups 18.3 (2013): 615-637.

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