共查询到20条相似文献,搜索用时 31 毫秒
1.
In this article we prove the Jacquet-Langlands local correspondence in non-zero characteristic. Let F be a local field of non-zero charactersitic and G′ an inner form of GLn(F); then, following [17], we prove relations between the representation theory of G′ and the representation theory of an inner form of GLn(L), where L is a local field of zero characteristic close to F. The proof of the Jacquet-Langlands correspondence between G′ and GLn(F) is done using the above results and ideas from the proof by Deligne, Kazhdan and Vignéras [10] of the zero characteristic case. We also get the following, already known in zero characteristic: orthogonality relations for G′, inequality involving conductor and level for representations of G′ and finiteness for automorphic cuspidal representations with fixed component at almost every place for an inner form of GLn over a global field of non-zero characteristic. 相似文献
2.
《代数通讯》2013,41(9):3367-3373
ABSTRACT Let D be a finite dimensional F -central division algebra and G an irreducible subgroup of D*: = GL 1(D). Here we investigate the structure of D under various group identities on G. In particular, it is shown that when [D:F] = p 2, p a prime, then D is cyclic if and only if D* contains a nonabelian subgroup satisfying a group identity. 相似文献
3.
Let F n be the free group of rank n, and let Aut+(F n ) be its special automorphism group. For an epimorphism π : F n → G of the free group F n onto a finite group G we call the standard congruence subgroup of Aut+(F n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ+(G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ+(G, π) ≤ Aut+(F 2) has infinite abelianization. 相似文献
4.
Anouar Saidi 《Journal of Mathematical Analysis and Applications》2010,363(2):618-626
Let G be a compact subgroup of GLn(R) acting linearly on a finite dimensional complex vector space E. B. Malgrange has shown that the space C∞G(Rn,E) of C∞ and G-covariant functions is a finite module over the ring C∞G(Rn) of C∞ and G-invariant functions. First, we generalize this result for the Schwartz space SG(Rn,E) of G-covariant functions. Secondly, we prove that any G-covariant distribution can be decomposed into a sum of G-invariant distributions multiplied with a fixed family of G-covariant polynomials. This gives a generalization of an Oksak result proved in [4]. 相似文献
5.
The cartesian product of a graph G with K2 is called a prism over G. We extend known conditions for hamiltonicity and pancyclicity of the prism over a graph G to the cartesian product of G with paths, cycles, cliques and general graphs. In particular we give results involving cubic graphs and almost claw-free graphs.We also prove the following: Let G and H be two connected graphs. Let both G and H have a 2-factor. If Δ(G)≤g′(H) and Δ(H)≤g′(G) (we denote by g′(F) the length of a shortest cycle in a 2-factor of a graph F taken over all 2-factorization of F), then G□H is hamiltonian. 相似文献
6.
We look at a special case of a familiar problem: Given a locally compact group G, a subgroup H and a complex representation π+ of G how does π+ decompose on restriction to H. Here G is GL+(2,F), where F is a nonarchimedian local field of characteristic not two, K a separable quadratic extension of F, GL+(2,F) the subgroup of index 2 in GL(2,F) consisting of those matrices whose determinant is in NK/F(K∗), π+ is an irreducible, admissible supercuspidal representation of GL+(2,F) and H=K∗ under an embedding of K∗ into GL(2,F). 相似文献
7.
Let D be an F-central division algebra of index n. Here we present a criterion for the triviality of the group G(D) = D*/Nrd D/F (D*)D′ and thus generalizing various related results published recently. To be more precise, it is shown that G(D) = 1 if and only if SK 1(D) = 1 and F *2 = F *2n . Using this, we investigate the role of some particular subgroups of D* in the algebraic structure of D. In this direction, it is proved that a division algebra D of prime index is a symbol algebra if and only if D* contains a non-abelian nilpotent subgroup. More applications of this criterion including the computation of G(D) and the structure of maximal subgroups of D* are also investigated 相似文献
8.
Michal Sadowski 《Central European Journal of Mathematics》2004,2(2):332-338
Let E
Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E
Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝ
m-n
. As an application we give some estimates of card E
Aff(Γ,G, m). 相似文献
9.
Katsusuke Sekiguchi 《代数通讯》2013,41(11):3611-3623
For a prime p, we denote by Bn the cyclic group of order pn. Let φ be a faithful irreducible character of Bn, where p is an odd prime. We study the p-group G containing Bn such that the induced character φG is also irreducible. The purpose of this article is to determine the subgroup NG(NG(Bn)) of G under the hypothesis [NG(Bn):Bn]4 ≦ pn. 相似文献
10.
Yossi Moshe 《Journal of Number Theory》2007,123(1):224-240
Let H(x) be a monic polynomial over a finite field F=GF(q). Denote by Na(n) the number of coefficients in Hn which are equal to an element a∈F, and by G the set of elements a∈F× such that Na(n)>0 for some n. We study the relationship between the numbers (Na(n))a∈G and the patterns in the base q representation of n. This enables us to prove that for “most” n's we have Na(n)≈Nb(n), a,b∈G. Considering the case H=x+1, we provide new results on Pascal's triangle modulo a prime. We also provide analogous results for the triangle of Stirling numbers of the first kind. 相似文献
11.
D. A. Malinin 《Algebras and Representation Theory》2003,6(2):215-237
For a given field F of characteristic 0 we consider a normal extension E/F of finite degree d and finite Abelian subgroups GGL
n
(E) of a given exponent t. We assume that G is stable under the natural action of the Galois group of E/F and consider the fields E=F(G) that are obtained via adjoining all matrix coefficients of all matrices gG to F. It is proved that under some reasonable restrictions for n, any E can be realized as F(G), while if all coefficients of matrices in G are algebraic integers, there are only finitely many fields E=F(G) for prescribed integers n and t or prescribed n and d. 相似文献
12.
We prove certain identities between Kloosterman integrals. They constitute the fundamental lemma of a relative trace formula for Hecke functions. The main application of the trace formula in question is the following result. Let E/F be a quadratic extension of number fields. A cuspidal automorphic representation of GL(n,EA) is distinguished by some unitary group if and only if it is the base change of an automorphic cuspidal representation of GL(n,FA). 相似文献
13.
Let F be a non-archimedean local field of odd residual characteristic. Let (J,τ) be a maximal simple type in GLN(F) for the inertial class [GLN(F),π]GLN(F) of a self-contragredient supercuspidal irreducible representation π of GLN(F). Identify GLN(F) to the standard Siegel Levi subgroup in Sp2N(F). We construct, in Sp2N(F), a type for the inertial class [GLN(F),π]Sp2N(F), as a Sp2N(F)-cover of (J,τ), strongly related to the GL2N(F)-cover of (J×J,τ⊗τ) in GL2N(F) constructed by Bushnell and Kutzko and which induces to a simple type in GL2N(F). In the process, we show that if τ has positive level, then the maximal simple type (J,τ) may be attached to a simple stratum [A,n,0,β] where the field F[β] is a quadratic extension of F[β2], and to a simple character θ in C(A,0,β) Galois conjugate of its inverse. 相似文献
14.
Joanna Raczek 《Discrete Mathematics》2008,308(23):5570-5575
Let G=(V,E) be a graph with δ(G)≥1. A set D⊆V is a paired dominating set if D is dominating, and the induced subgraph 〈D〉 contains a perfect matching. The paired domination number of G, denoted by γp(G), is the minimum cardinality of a paired dominating set of G. The paired bondage number, denoted by bp(G), is the minimum cardinality among all sets of edges E′⊆E such that δ(G−E′)≥1 and γp(G−E′)>γp(G). We say that G is a γp-strongly stable graph if, for all E′⊆E, either γp(G−E′)=γp(G) or δ(G−E′)=0. We discuss the basic properties of paired bondage and give a constructive characterization of γp-strongly stable trees. 相似文献
15.
Let G be a finite group having a faithful irreducible character χ for which χ(1) is prime to ¦G¦/χ(1). Let n=[(χ):]χ(1), and assume that the factors are not both even. Then G can be embedded in GLn() in such a way that its normalizer therein splits over its centralizer. 相似文献
16.
D.A. Shmelkin 《Advances in Mathematics》2002,167(2):175-194
Let U(G) be a maximal unipotent subgroup of one of the classical groups G=GL(V), O(V), Sp(V). Let W be a direct sum of copies of V and its dual V*. For the natural action U(G) : W, we describe a minimal system of homogeneous generators for the algebra of U(G)-invariant regular functions on W. For G=O(V), Sp(V), this result is connected with a construction for the irreducible representations of G due to H. Weyl. 相似文献
17.
Let D be an infinite division ring. A famous result due to Herstein says that every non-central element of D has infinitely many conjugates and so, if D
* is an FC-group, then D is a field. Let M be a maximal subgroup of GL
n
(D), where n ≥ 1. In this paper, we prove that if M is an FC-group, then it is the multiplicative group of some maximal subfield of M
n
(D). Moreover, if M is algebraic over Z(D), then [D : Z(D)] < ∞. 相似文献
18.
Let D(G) be the minimum quantifier depth of a first order sentence Φ that defines a graph G up to isomorphism. Let D0(G) be the version of D(G) where we do not allow quantifier alternations in Φ. Define q0(n) to be the minimum of D0(G) over all graphs G of order n.We prove that for all n we have
log*n−log*log*n−2≤q0(n)≤log*n+22,