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On the existence of a unipotent support for the irreducible characters of a finite group of Lie type
In 1980, Lusztig posed the problem of showing the existence of a unipotent support for the irreducible characters of a finite group of Lie type. This problem was solved by Lusztig in the case where the characteristic of the field over which the group is defined is large enough. The first named author extended this to the case where the characteristic is good. It is the purpose of this paper to remove this condition as well, so that the existence of unipotent supports is established in complete generality.
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We present a black-box polynomial-time Monte Carlo algorithmwhich, given as input a quasi-simple group of Lie type, findsits characteristic. 相似文献
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We show that the kernel of an irreducible unitary representation π of the group algebra L1(G) of a completely solvable Lie group G is given by the functions, whose abelian Fourier transform vanish on the Kirillov orbit Oπ of π if and only if this orbit Oπ is flat. This is a generalization of a result obtained before for nilpotent Lie groups. 相似文献
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Donald W. Barnes 《代数通讯》2019,47(8):3198-3201
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Henrik Schlichtkrull 《Inventiones Mathematicae》1982,68(3):497-516
LetG/H be a semisimple symmetric space. Generalizing results of Flensted-Jensen we give a sufficient condition for the existence of irreducible closed invariant subspaces of the unitary representations ofG induced from unitary finite dimensional representations ofH. This provides a method of constructing unitary irreducible representations ofG, and we show by examples that for some irreducible admissible representations ofG, this method exhibits not previously known unitarity.This work was supported by the Danish Natural Science Research Council. 相似文献
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