On the centralizer of a regular, semi-simple, stable conjugacy class

Gross, Benedict

doi:10.1090/S1088-4165-05-00283-9

On the centralizer of a regular, semi-simple, stable conjugacy class

Author: Benedict H. Gross
Journal: Represent. Theory 9 (2005), 287-296
MSC (2000): Primary 20G15
DOI: https://doi.org/10.1090/S1088-4165-05-00283-9
Published electronically: April 8, 2005
MathSciNet review: 2133761
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We describe the isomorphism class of the torus centralizing a regular, semi-simple, stable conjugacy class in a simply-connected, semi-simple group.

[G-Mc] Benedict H. Gross and Curtis T. McMullen, Automorphisms of even unimodular lattices and unramified Salem numbers, J. Algebra 257 (2002), no. 2, 265–290. MR 1947324, https://doi.org/10.1016/S0021-8693(02)00552-5
[G-P] Benedict H. Gross and David Pollack, On the Euler characteristic of the discrete spectrum, J. Number Theory 110 (2005), no. 1, 136–163. MR 2114678, https://doi.org/10.1016/j.jnt.2004.03.008
[K] Robert E. Kottwitz, Rational conjugacy classes in reductive groups, Duke Math. J. 49 (1982), no. 4, 785–806. MR 683003
[Se] Jean-Pierre Serre, Cohomologie galoisienne, 5th ed., Lecture Notes in Mathematics, vol. 5, Springer-Verlag, Berlin, 1994 (French). MR 1324577
[Se2] Jean-Pierre Serre, L’invariant de Witt de la forme 𝑇𝑟(𝑥²), Comment. Math. Helv. 59 (1984), no. 4, 651–676 (French). MR 780081, https://doi.org/10.1007/BF02566371
[S-S] T. A. Springer and R. Steinberg, Conjugacy classes, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69) Lecture Notes in Mathematics, Vol. 131, Springer, Berlin, 1970, pp. 167–266. MR 0268192
[S] Robert Steinberg, Regular elements of semisimple algebraic groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 49–80. MR 180554