Permutation characters of finite groups of Lie type
1979 ◽
Vol 27
(3)
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pp. 378-384
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Keyword(s):
AbstractLet g be a connected reductive linear algebraic group, and let G = gσ be the finite subgroup of fixed points, where σ is the generalized Frobenius endomorphism of g. Let x be a regular semisimple element of G and let w be a corresponding element of the Weyl group W. In this paper we give a formula for the number of right cosets of a parabolic subgroup of G left fixed by x, in terms of the corresponding action of w in W. In case G is untwisted, it turns out thta x fixes exactly as many cosets as does W in the corresponding permutation representation.
2008 ◽
Vol 4
(1)
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pp. 91-100
Keyword(s):
1971 ◽
Vol 12
(1)
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pp. 1-14
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1990 ◽
Vol 49
(3)
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pp. 449-485
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Keyword(s):
2002 ◽
Vol 34
(2)
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pp. 165-173
1983 ◽
Vol 27
(3)
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pp. 361-379
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Keyword(s):
2007 ◽
Vol 10
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pp. 329-340
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Keyword(s):
2010 ◽
Vol 21
(12)
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pp. 1633-1638
Keyword(s):
1993 ◽
Vol 337
(1)
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pp. 211-218
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Keyword(s):