The Weyl map and bundle gerbes

Abstract

We introduce the notion of a general cup product bundle gerbe and use it to define the Weyl bundle gerbe on T x SU(n)/T. The Weyl map from T x SU(n)/T to SU(n) is then used to show that the pullback of the basic bundle gerbe on SU(n) defined by the second two authors is stably isomorphic to the Weyl bundle gerbe as SU(n)-equivariant bundle gerbes. Both bundle gerbes come equipped with connections and curvings and by considering the holonomy of these we show that these bundle gerbes are not D-stably isomorphic.

This paper is based on the MPhil thesis of the first author: arXiv:1910.01776. To appear in Journal of Geometry and Physics

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• Constructions with bundle gerbes
• The index of projective families of elliptic operators: the decomposable case
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• Geometry of Pseudodifferential algebra bundles and Fourier Integral Operators
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Cited by in corpus (2)

• Many finite-dimensional lifting bundle gerbes are torsion
• Spectral Sequence Computation of Higher Twisted $K$-Groups of $SU(n)$