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Archiv der Mathematik

, Volume 107, Issue 2, pp 101–119 | Cite as

Essential dimension of algebraic groups, including bad characteristic

  • Skip Garibaldi
  • Robert M. Guralnick
Article

Abstract

We give upper bounds on the essential dimension of (quasi-) simple algebraic groups over an algebraically closed field that hold in all characteristics. The results depend on showing that certain representations are generically free. In particular, aside from the cases of spin and half-spin groups, we prove that the essential dimension of a simple algebraic group G of rank at least two is at most dim G - 2(rank G) - 1. It is known that the essential dimension of spin and half-spin groups grows exponentially in the rank. In most cases, our bounds are as good as or better than those known in characteristic zero and the proofs are shorter. We also compute the generic stabilizer of an adjoint group on its Lie algebra.

Mathematics Subject Classification

Primary 11E72 Secondary 20G41 17B45 

Keywords

Essential dimension Adjoint representation Generic stabilizer 

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Copyright information

© Springer International Publishing (outside the USA) 2016

Authors and Affiliations

  1. 1.Center for Communications ResearchSan DiegoUSA
  2. 2.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA

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