248 research outputs found
Abstract involutions of algebraic groups and of Kac-Moody groups
Based on the second author's thesis in this article we provide a uniform
treatment of abstract involutions of algebraic groups and of Kac-Moody groups
using twin buildings, RGD systems, and twisted involutions of Coxeter groups.
Notably we simultaneously generalize the double coset decompositions
established by Springer and by Helminck-Wang for algebraic groups and by
Kac-Wang for certain Kac-Moody groups, we analyze the filtration studied by
Devillers-Muhlherr in the context of arbitrary involutions, and we answer a
structural question on the combinatorics of involutions of twin buildings
raised by Bennett-Gramlich-Hoffman-Shpectorov
On Lusztig's map for spherical unipotent conjugacy classes
We provide an alternative description of the restriction to spherical
unipotent conjugacy classes, of Lusztig's map Psi from the set of unipotent
conjugacy classes in a connected reductive algebraic group to the set of
conjugacy classes of its Weyl group. For irreducible root systems, we analyze
the image of this restricted map and we prove that a conjugacy class in a
finite Weyl group has a unique maximal length element if and only if it has a
maximum.Comment: Refereed version, one reference added. The final version will appear
in the Bulletin of the London Mathematical Societ
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