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arXiv · 1303.2195

Conformal symmetries of the super Dirac operator

Kevin Coulembier·Hendrik De Bie
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Abstract

In this paper, the Dirac operator, acting on super functions with values in super spinor space, is defined along the lines of the construction of generalized Cauchy-Riemann operators by Stein and Weiss. The introduction of the superalgebra of symmetries osp(m|2n) is a new and essential feature in this approach. This algebra of symmetries is extended to the algebra of conformal symmetries osp(m + 1, 1|2n). The kernel of the Dirac operator is studied as a representation of both algebras. The construction also gives an explicit realization of the Howe dual pair osp(1|2) x osp(m|2n) < osp(m + 4n|2m + 2n). Finally, the super Dirac operator gives insight into the open problem of classifying invariant first order differential operators in super parabolic geometries.

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Kevin Coulembier, Hendrik De Bie. 2013-03-09. Conformal symmetries of the super Dirac operator. https://arxiv.org/abs/1303.2195

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