Quotients for sheets of conjugacy classes
Giovanna Carnovale, Francesco Esposito

TL;DR
This paper characterizes the orbit space of sheets of conjugacy classes in complex simple algebraic groups, establishing a bijection with a quotient of a shifted torus and analyzing the normality of categorical quotients.
Contribution
It provides a novel description of the orbit space of sheets for conjugation actions, extending previous results and including detailed examples like G2.
Findings
Describes the orbit space of sheets via a bijection with a quotient of a shifted torus.
Provides conditions for the normality of the categorical quotient of sheets.
Works out detailed example for the group G2.
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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Taxonomy
TopicsAdvanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
