Lie subalgebras of differential operators on the super circle

2001/03/15 by Shun-Jen Cheng, Weiqiang Wang · 1 citation
Mathematics · #math.QA #msc:17B65

paper · pdf

published as Publ. Res. Inst. Math. Sci. 39 (2003), No. 3, 545--600 · 51 pages, Latex format

arxiv created 2001/03/15 · arxiv updated 2009/11/30

Abstract

We classify anti-involutions of Lie superalgebra \hsd preserving the principal gradation, where \hsd is the central extension of the Lie superalgebra of differential operators on the super circle S^1|1. We clarify the relations between the corresponding subalgebras fixed by these anti-involutions and subalgebras of gl_∞|∞ of types OSP and P. We obtain a criterion for an irreducible highest weight module over these subalgebras to be quasifinite and construct free field realizations of a distinguished class of these modules. We further establish dualities between them and certain finite-dimensional classical Lie groups on Fock spaces.

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