共查询到20条相似文献,搜索用时 46 毫秒
1.
Wang Dengyin 《Linear and Multilinear Algebra》2005,53(5):375-386
All parabolic subgroups and Borel subgroups of PSp(2m, F) over a linearable field F are shown to be complete groups. 相似文献
2.
Hou zixin 《数学年刊B辑(英文版)》1992,13(4):440-454
The author defines the large type Borel subgroups of a reductive algebraic goup,which are used to discuss Langlands' L-goups and the Langlands classification of the admissible representations of reductive algebraic groups over R(see[1,2,5]) and determine all of the Borel subgroups of large type for the classical semisimple Lie groups. 相似文献
3.
王登银 《数学物理学报(B辑英文版)》2007,27(2):317-328
All parabolic subgroups and Borel subgroups of PΩ(2m 1, F) over a linear-able field F of characteristic 0 are shown to be complete groups, provided m > 3. 相似文献
4.
We investigate the Borelness of the product of two Borel subgroups in Polish groups. While the intersection of these two subgroups is Polishable, the Borelness of their product is confirmed. On the other hand, we construct two subgroups whose product is not Borel in every uncountable abelian Polish group.
5.
Rose Morris-Wright 《Journal of Pure and Applied Algebra》2021,225(1):106468
Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic. 相似文献
6.
7.
V. V. Korableva 《Siberian Mathematical Journal》2008,49(2):273-286
We determine the ranks of the permutation representations of the simple groups B l (q), C l (q), and D l (q) on the cosets of the parabolic maximal subgroups. 相似文献
8.
Sankaran Viswanath 《代数通讯》2013,41(2):796-805
The principal objects studied in this note are infinite, non-affine Coxeter groups W. A well-known result of de la Harpe asserts that such groups have exponential growth. We study the growth type of quotients of W by parabolic subgroups and by a certain class of reflection subgroups. Our main result is that these quotients have exponential growth as well. 相似文献
9.
Waldemar Holubowski 《Proceedings of the American Mathematical Society》2002,130(9):2579-2582
In this note we show that all parabolic subgroups of Vershik-Kerov's group (i.e. subgroups containing --the group of infinite dimensional upper triangular matrices) are net subgroups for a wide class of semilocal rings .
10.
V. V. Korableva 《Algebra and Logic》2010,49(3):246-255
Ranks, degrees, subdegrees, and double stabilizers of permutation representations for finite symplectic groups are defined
on cosets with respect to maximal parabolic subgroups. 相似文献
11.
V. V. Korableva 《Proceedings of the Steklov Institute of Mathematics》2009,267(1):100-110
The ranks, degrees, subdegrees, and double stabilizers of permutation representations of finite special linear and unitary groups on cosets of parabolic maximal subgroups are found. 相似文献
12.
V. V. Korableva 《Algebra and Logic》2010,49(5):416-425
Ranks, degrees, subdegrees, and double stabilizers of permutation representations for finite simple orthogonal groups in odd
dimensions are defined on cosets with respect to maximal parabolic subgroups. 相似文献
13.
14.
Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups
of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and
as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank
play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions
dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups
may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers
of those quasisimple groups are structured. The present paper is devoted to tackling this problem.
Supported by RFBR (grant No. 05-01-00797) and by SB RAS (Young Researchers Support grant No. 29 and Integration project No.
2006.1.2).
__________
Translated from Algebra i Logika, Vol. 47, No. 1, pp. 3–30, January–February, 2008. 相似文献
15.
Shin-ichi Kato 《Journal of Functional Analysis》2010,258(5):1427-1451
A symmetric space analogue of Casselman's criterion for square integrability of representations of a p-adic group is established. It is described in terms of exponents of Jacquet modules along parabolic subgroups associated to the symmetric space. 相似文献
16.
R. I. Grigorchuk 《Mathematical Notes》2000,67(6):718-723
The class of branch groups is defined (both in the abstract and in the profinite category). The relationship of this class
with the class of extremal groups is established. Properties of the branch groups are investigated. Applications of the congruence
property to the theory of profinite branch groups are indicated. The weak maximality of parabolic subgroups in branch groups
is proved.
Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 852–858, June, 2000. 相似文献
17.
《代数通讯》2013,41(7):3471-3486
Abstract Taking G to be a Chevalley group of rank at least 3 and U to be the unipotent radical of a Borel subgroup B,an extremal subgroup A is an abelian normal subgroup of U which is not contained in the intersection of all the unipotent radicals of the rank 1 parabolic subgroups of G containing B. If there is an unique rank 1 parabolic subgroup P of G containing B with the property that A is not contained in the unipotent radical of P,then A is called a unique node extremal subgroup. In this paper we investigate the embedding of unique node extremal subgroups in U and prove that,apart from some specified cases,such a subgroup is contained in the unipotent radical of a certain maximal parabolic subgroup. 相似文献
18.
For geometries associated with permutation representations of the groups of Lie type E
6, E
7, E
8 on certain maximal parabolic subgroups (e.g. the stabilizers of root subgroups), axiom systems are given that characterize them in terms of points and lines. 相似文献
19.
Joseph A. Wolf 《Mathematische Annalen》2013,357(3):895-914
We study the conditions for a nilpotent Lie group to be foliated into subgroups that have square integrable (relative discrete series) unitary representations, that fit together to form a filtration by normal subgroups. Then we use that filtration to construct a class of “stepwise square integrable” representations on which Plancherel measure is concentrated. Further, we work out the character formulae for those stepwise square integrable representations, and we give an explicit Plancherel formula. Next, we use some structure theory to check that all these constructions and results apply to nilradicals of minimal parabolic subgroups of real reductive Lie groups. Finally, we develop multiplicity formulae for compact quotients $N/\varGamma $ where $\varGamma $ respects the filtration. 相似文献
20.
Céline Righi 《Journal of Algebra》2008,319(4):1555-1584
We extend the results of Cellini and Papi [P. Cellini, P. Papi, Ad-nilpotent ideals of a Borel subalgebra, J. Algebra 225 (2000) 130–140; P. Cellini, P. Papi, Ad-nilpotent ideals of a Borel subalgebra II, J. Algebra 258 (2002) 112–121] on the characterizations of ad-nilpotent and abelian ideals of a Borel subalgebra to parabolic subalgebras of a simple Lie algebra. These characterizations are given in terms of elements of the affine Weyl group and faces of alcoves. In the case of a parabolic subalgebra of a classical simple Lie algebra, we give formulas for the number of these ideals. 相似文献