Component groups of unipotent centralizers in good characteristic
By George J. McNinch, E. Sommers. 2002
63 citations recorded by the source corpus.
Abstract Let G be a connected, reductive group over an algebraically closed field of good characteristic. For u ∈ G unipotent, we describe the conjugacy classes in the component group A ( u ) of the centralizer of u . Our results extend work of the second author done for simple, adjoint G over the complex numbers. When G is simple and adjoint, the previous work of the second author makes our description combinatorial and explicit; moreover, it turns out that knowledge of the conjugacy classes suffices to determine the group structure of A ( u ). Thus we obtain the result, previously known through case-checking, that the structure of the component group A ( u ) is independent of good characteristic.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bf2006393b107be3626ec45c2a16beb65c0369ca
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
In Geometry and Topology
- D. Testerman
- R. Lawther
- Paul Blain Levy
- A. Premet
- George J. McNinch
- I. Losev
- V. Ginzburg
- Alexander S. Kleshchev
In Mathematical Physics
- D. Testerman
- R. Lawther
- Paul Blain Levy
- A. Premet
- George J. McNinch
- I. Losev
- V. Ginzburg
- Jonathan Brundan
Citations in the corpus
- Nilpotent orbits over ground fields of good characteristic (2002, background): “[SS70, 3.19] (this could also be deduced from the explicit results in [ MS ]).”
- Enveloping algebras of Slodowy slices and the Joseph ideal (2005, background): “As AdG is a group of adjoint type, the G-conjugacy class of the pair (L, e) corresponds under Sommers’ bijection to the G-conjugacy class of the pair (e, C); see [34, 27, 31].”
- Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups (2011, background): “For the structure of the finite group A, we refer to [6, 25].”
- Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices (2009, methodology): “For p good, the possible root systems for such subgroups are given by proper subsets of the extended Dynkin diagram of G, see [So, Prop. 2] in characteristic zero, [ MS , Prop.”