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Yasushi Gomi 《代数通讯》2013,41(1):123-138
The purpose of this paper is to calculate all the character tables of Hecke algebras associated with exceptional Weyl groups and their maximal parabolic subgroups when they are commutative. In the case when Weyl groups are of classical type, they are already known in [D.1] and [D.2]. In §1, we discuss the structure of Hecke algebras and in §2, we calculate all the character tables of these commutative Hecke algebras associated with exceptional Weyl groups.  相似文献   

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We determine the 2-modular character table of the Fischer group Fi23.  相似文献   

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In this note, we prove the following result, settling a question raised at the end of [Borel & Serre 1953], cf. [Borel 1983 pp. 228 and 708]. A related result for Lie groups of type E8 was recently proved by J.F. Adams.  相似文献   

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Let G be a connected reductive complex Lie group. Let E G be the image of the exponential map of G and E' G its complement in G. We give a purely algebraic characterization of the set E G and also describe an algorithm for finding all conjugacy classes of G in E' G . We are mainly interested in the case when the Lie algebra of G is simple and exceptional. Full details are provided for groups G of type G 2, F 4, and E 6. If G is of type G 2 then there are only two such conjugacy classes.This work was supported by NSERC Grant A-5285.  相似文献   

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Let G be a simple, simply connected algebraic group of exceptional type defined over Fq with Frobenius endomorphism F:GG. Let ??q be a good prime for G. We determine the number of irreducible Brauer characters in the quasi-isolated ?-blocks of GF. This is done by proving that generalized e-Harish-Chandra theory holds for the Lusztig series associated to quasi-isolated elements of G?F.  相似文献   

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We study finite subgroups of exceptional groups of Lie type, in particular maximal subgroups. Reduction theorems allow us to concentrate on almost simple subgroups, the main case being those with socle of Lie type in the natural characteristic. Our approach is to show that for sufficiently large (usually suffices), is contained in a subgroup of positive dimension in the corresponding exceptional algebraic group, stabilizing the same subspaces of the Lie algebra. Applications are given to the study of maximal subgroups of finite exceptional groups. For example, we show that all maximal subgroups of sufficiently large order arise as fixed point groups of maximal closed subgroups of positive dimension.

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A class of graded simple associative algebras are constructed, and from them, simple Lie color algebras are obtained. The structure of these simple Lie color algebras is explicitly described. More precisely, for an (ε, Γ)-color-commutative associative algebraA with an identity element over a fieldF of characteristic not 2, and for a color-commutative subalgebraD of color-derivations ofA, denote byA[D] the associative subalgebra of End (A) generated byA (regarded as operators onA via left multiplication) andD. It is easily proved that, as an associative algebra,A[D] is Γ-graded simple if and only ifA is Γ-gradedD-simple. SupposeA is Γ-gradedD-simple. Then, (a)A[D] is a free leftA-module; (b) as a Lie color algebra, the subquotient [A[D],A[D]]/Z(A[D])∩[A[D],A[D]] is simple (except one minor case), whereZ(A[D]) is the color center ofA[D]. This work was supported by NSF of China, National Educational Department of China, Jiangsu Educational Committee, and Hundred Talents Program of Chinese Academy of Sciences. These authors were partially supported by Academy of Mathematics and System Sciences during their visit to this academy.  相似文献   

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In this note we prove the mod 2 cohomology of an exceptional Lie group can be computed from the rational cohomology. In fact the rational cohomology determines the mod 2 cohomology as an algebra over the Steenrod algebra.  相似文献   

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Maximal subgroups of exceptional groups of Lie type,finite and algebraic   总被引:4,自引:0,他引:4  
The maximal closed subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields are determined, subject to certain restrictions on the characteristic. This result is used to prove a reduction theorem for maximal subgroups of finite exceptional groups of Lie type: such a subgroup is either of known type, or it is almost simple. Finally, the generic almost simple maximal subgroups are determined for large characteristic.Dedicated to Professor J. Tits on the occasion of his sixtieth birthdaySupported in part by NSF and NSA grants and an SERC visiting fellowship at Imperial College, London.  相似文献   

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