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arXiv · 1801.06915

Generically free representations III: extremely bad characteristic

Skip Garibaldi·Robert M. Guralnick
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Abstract

In parts I and II, we determined which faithful irreducible representations $V$ of a simple linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$ have an open subset consisting of vectors whose stabilizer in Lie($G$) is zero, with some assumptions on the characteristic of the field. This paper settles the remaining cases, which are of a different nature because Lie($G$) has a more complicated structure and there need not exist general dimension bounds of the sort that exist in good characteristic.

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Skip Garibaldi, Robert M. Guralnick. 2019-04-17. Generically free representations III: extremely bad characteristic. https://doi.org/10.1007/s00031-020-09590-4

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