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Birational sheets in reductive groups · arXivDesk

2002.11551Feb 26, 202025 pages, to appear in Math. Z. A distinction between birational sheets and weakly birational sheets has been introduced. Key modifications/additions: Definition 3.8, Remark 4.4, Subsection 5.1, Remark 5.4, Example 5.5, Remark 5.17, Subsection 5.4, Theorem 6.8

Birational sheets in reductive groups

Filippo Ambrosio

Representation Theory Group Theory

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Abstract

We define the group analogue of birational sheets, a construction performed by Losev for reductive Lie algebras. For G semisimple simply connected, we describe birational sheets in terms of Lusztig-Spaltenstein induction and we prove that they form a partition of G, and that they are unibranch varieties with smooth normalization by means of a local study.

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The paper addresses: Birational sheets in reductive groups.
We define the group analogue of birational sheets, a construction performed by Losev for reductive Lie algebras.

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Author comment: 25 pages, to appear in Math. Z. A distinction between birational sheets and weakly birational sheets has been introduced. Key modifications/additions: Definition 3.8, Remark 4.4, Subsection 5.1, Remark 5.4, Example 5.5, Remark 5.17, Subsection 5.4, Theorem 6.8