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arXiv · 1802.00988

Quotients for sheets of conjugacy classes

Giovanna Carnovale·Francesco Esposito
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Abstract

We provide a description of the orbit space of a sheet S for the conjugation action of a complex simple simply connected algebraic group G. This is obtained by means of a bijection between S/G and the quotient of a shifted torus modulo the action of a subgroup of the Weyl group and it is the group analogue of a result due to Borho and Kraft. We also describe the normalisation of the categorical quotient \overline{S}//G for arbitrary simple G and give a necessary and sufficient condition for S//G to be normal in analogy to results of Borho, Kraft and Richardson. The example of G_2 is worked out in detail.

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BibTeXRIS

Giovanna Carnovale, Francesco Esposito. 2018-02-03. Quotients for sheets of conjugacy classes. https://arxiv.org/abs/1802.00988

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