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arXiv · 1209.6132

A commutant realization of Odake's algebra

Thomas Creutzig·Andrew R. Linshaw
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Abstract

The bcβγ-system W of rank 3 has an action of the affine vertex algebra V_0(sl_2), and the commutant vertex algebra C =Com(V_0(sl_2), W) contains copies of V_{-3/2}(sl_2) and Odake's algebra O. Odake's algebra is an extension of the N=2 superconformal 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}(sl_2) 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 sl_2.

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BibTeXRIS

Thomas Creutzig, Andrew R. Linshaw. 2013-07-11. A commutant realization of Odake's algebra. https://doi.org/10.1007/s00031-013-9235-8

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