JournalsprimsVol. 39, No. 3pp. 545–600

Lie Subalgebras of Differential Operators on the Super Circle

  • Shun-Jen Cheng

    Academia Sinica, Taipei, Taiwan
  • Weiqiang Wang

    University of Virginia, Charlottesville, USA
Lie Subalgebras of Differential Operators on the Super Circle cover
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Abstract

We classify anti-involutions of Lie superalgebra SD preserving the principal gradation, where SD 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.

Cite this article

Shun-Jen Cheng, Weiqiang Wang, Lie Subalgebras of Differential Operators on the Super Circle. Publ. Res. Inst. Math. Sci. 39 (2003), no. 3, pp. 545–600

DOI 10.2977/PRIMS/1145476079