共查询到17条相似文献,搜索用时 62 毫秒
1.
记Φ为低欧氏空间V中某不可约根系,具有Weyl群W,记σ为W中满足条件ω(Φ^+)=Φ^-的唯一元。本考虑如何将σ分解成反射之积;σ在Φ上的作用方式如何。作为应用确定了W的中心;进一步确定了V的一类子空间在W中的固定子群。 相似文献
2.
3.
本文决定了 Dl 和 E6 型 Weyl群扭子群的所有扩群 ,这为确定相应 Chevalley群扭子群的所有扩群奠定了基础 . 相似文献
4.
Chevalley群的一类子群的研究 总被引:1,自引:0,他引:1
设G=L(F)是特征不为2的域F上Chevalley群,型为B1(l≥4),Cl(l≥3),Dl(l≥5),E6,E7,E8或F4之一.当L(F)型为B4或F4时还假设F=F2设Lα1是L(F)的一类Levy子群.本文决定Lα1的正规化子在L(F)中的极大性. 相似文献
5.
本决定了D1和E6型Weyl群扭子群的所有扩群,这为确定相应Chevalley群扭子群的所有扩群奠定了基础。 相似文献
6.
7.
8.
weyl群的定义关系及其应用 总被引:1,自引:0,他引:1
首 先深化 R. Steinberg 关于 W eyl 群定义 关系的一个定 理,作为应 用,对 Bl , Cl 型 W eyl群分别构造了一 个指数为2的正 规子群 相似文献
9.
本文首先给出Kac-Moody代数IXr(a)的有限型IC or (a)的未定Weyl群的定义,然后对a≥5证明了不定型李代数IXr(a)的Weyl群W同构于有限型IXr(a)的未定Weyl群. 相似文献
10.
本文首先给出Kac-Moody代数IXr(a)的有限型I(?)r(a)的未定Weyl群的定义,然后对a≥5证明了不定型李代数,IXr(a)的Weyl群W同构于有限型I(?)r(a)的未定Weyl群. 相似文献
11.
Elizabeth Wiggins 《代数通讯》2013,41(9):4001-4025
Let G be a simply connected, semisimple algebraic group of type B4 or D4 over an algebraically closed field of characteristic p > 0. We determine the characters of certain simple modules for these groups by calculating the composition factors of the Weyl modules. 相似文献
12.
Amy E. Ksir 《Algebras and Representation Theory》1999,2(3):249-258
Let W be a Weyl group and P W, a parabolic subgroup. In this paper, we give the decomposition of the permutation representation Ind
P
W
1 into irreducibles for each exceptional W and maximal parabolic P. We find that there is an 'extra' common irreducible component which appears for exceptional groups and not for classical groups. This work is motivated by the study of Prym varieties and integrable systems. 相似文献
13.
We give several necessary and sufficient conditions for the existence of the presentation by conjugation for a non-simply laced extended affine Weyl group. We invent a computational tool by which one can determine simply the existence of the presentation by conjugation for an extended affine Weyl group. As an application, we determine the existence of the presentation by conjugation for a large class of extended affine Weyl groups. 相似文献
14.
We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley Theorem for their invariants, and construct a Frobenius structure on their orbit spaces. This produces solutions F(t1, ..., tn) of WDVV equations of associativity polynomial in t1, ..., tn-1, exp tn. 相似文献
15.
16.
Karl H. Hofmann Jimmie D. Lawson Wolfgang A. F. Ruppert 《Mathematische Nachrichten》1996,179(1):119-143
For each pair (??,??) consisting of a real Lie algebra ?? and a subalgebra a of some Cartan subalgebra ?? of ?? such that [??, ??]∪ [??, ??] we define a Weyl group W(??, ??) and show that it is finite. In particular, W(??, ??,) is finite for any Cartan subalgebra h. The proof involves the embedding of 0 into the Lie algebra of a complex algebraic linear Lie group to which the structure theory of Lie algebras and algebraic groups is applied. If G is a real connected Lie group with Lie algebra ??, the normalizer N(??, G) acts on the finite set Λ of roots of the complexification ??c with respect to hc, giving a representation π : N(??, G)→ S(Λ) into the symmetric group on the set Λ. We call the kernel of this map the Cartan subgroup C(??) of G with respect to h; the image is isomorphic to W(??, ??), and C(??)= {g G : Ad(g)(h)— h ε [h,h] for all h ε h }. All concepts introduced and discussed reduce in special situations to the familiar ones. The information on the finiteness of the Weyl groups is applied to show that under very general circumstance, for b ∪ ?? the set ??? ?(b) remains finite as ? ranges through the full group of inner automorphisms of ??. 相似文献
17.
Debra J. Waugh 《Order》1999,16(1):77-87
Björner and Wachs proved that under the weak order every quotient of a Coxeter group is a meet semi-lattice, and in the finite case is a lattice. In this paper, we examine the case of an affine Weyl group W with corresponding finite Weyl group W
0. In particular, we show that the quotient of W by W
0 is a lattice and that up to isomorphism this is the only quotient of W which is a lattice. We also determine that the question of which pairs of elements of W have upper bounds can be reduced to the analogous question within a particular finite subposet. 相似文献