共查询到20条相似文献,搜索用时 15 毫秒
1.
Hiroyuki Ishibashi 《Journal of Pure and Applied Algebra》1981,22(2):121-129
This paper is devoted to determine the minimal length of expressions of an isometry in a symplectic group Spn(V) by a product of transvections under the assumption that V is an n-ary nonsingular alternating space over a quasi semilocal semihereditary ring with 2 as a unit. 相似文献
2.
Let R denote a commutative local ring with maximal ideal m and residue field K = R/m. Let V be a symplectic space over R. In this paper we determine the group automorphisms of the symplectic group Spn(V) when n 6, the characteristic of k is not 2, and k is not the finite field of three elements. 相似文献
3.
S. Tazhetdinov 《Mathematical Notes》2006,80(5-6):726-728
4.
D.E. Littlewood proved two branching theorems for decomposing the restriction of an irreducible finite-dimensional representation of a unitary group to a symmetric subgroup. One is for restriction of a representation of U(n) to the rotation group SO(n) when the given representation τλ of U(n) has nonnegative highest weight λ of depth n/2. It says that the multiplicity in τλ|SO(n) of an irreducible representation of SO(n) of highest weight ν is the sum over μ of the multiplicities of τλ in the U(n) tensor product τμτν, the allowable μ's being all even nonnegative highest weights for U(n). Littlewood's proof is character-theoretic. The present paper gives a geometric interpretation of this theorem involving the tensor products τμτν explicitly. The geometric interpretation has an application to the construction of small infinite-dimensional unitary representations of indefinite orthogonal groups and, for each of these representations, to the determination of its restriction to a maximal compact subgroup. The other Littlewood branching theorem is for restriction from U(2r) to the rank-r quaternion unitary group Sp(r). It concerns nonnegative highest weights for U(2r) of depth r, and its statement is of the same general kind. The present paper finds an analogous geometric interpretation for this theorem also. 相似文献
5.
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
6.
A. Benhocine 《Discrete Mathematics》1978,22(3):213-217
Given two directed graphs G1, G2, the Ramsey number R(G1,G2) is the smallest integer n such that for any partition {U1,U2} of the arcs of the complete symmetric directed graph K1n, there exists an integer i such that the partial graph generated by Ui contains Gi as a subgraph. In this article, we determine R(P?m,D?n) and R(D?m,D?n) for some values of m and n, where P?m denotes the directed path having m vertices and D?m is obtained from P?m by adding an arc from the initial vertex of P?m to the terminal vertex. 相似文献
7.
In this article, we verify Dade's projective invariant conjecture for the symplectic group Sp4(2 n ) and the special unitary group SU4(22n ) in the defining characteristic, that is, in characteristic 2. Furthermore, we show that the Isaacs–Malle–Navarro version of the McKay conjecture holds for Sp4(2 n ) and SU4(22n ) in the defining characteristic, that is, Sp4(2 n ) and SU4(22n ) are good for the prime 2 in the sense of Isaacs, Malle, and Navarro. 相似文献
8.
Tiefeng Jiang 《Journal of Theoretical Probability》2010,23(4):1227-1243
Let Γ
n
=(γ
ij
)
n×n
be a random matrix with the Haar probability measure on the orthogonal group O(n), the unitary group U(n), or the symplectic group Sp(n). Given 1≤m<n, a probability inequality for a distance between (γ
ij
)
n×m
and some mn independent F-valued normal random variables is obtained, where F=ℝ, ℂ, or ℍ (the set of real quaternions). The result is universal for the three cases. In particular, the inequality for
Sp(n) is new. 相似文献
9.
In this paper, we give the eigenvalues of the manifold Sp(n)/U(n). We prove that an eigenvalue λ
s
(f
2, f
2, …, f
n
) of the Lie group Sp(n), corresponding to the representation with label (f
1, f
2, ..., f
n
), is an eigenvalue of the manifold Sp(n)/U(n), if and only if f
1, f
2, …, f
n
are all even. 相似文献
10.
Let V be a 6-dimensional vector space over a field F, let f be a nondegenerate alternating bilinear form on V and let Sp(V,f)≅Sp6(F) denote the symplectic group associated with (V,f). The group GL(V) has a natural action on the third exterior power ?3V of V and this action defines five families of nonzero trivectors of V (four of whose are orbits for any choice of F). In this paper, we divide three of these five families into orbits for the action of Sp(V,f)⊆GL(V) on ?3V. 相似文献
11.
A. Gómez-Tato E. Macías-Virgós M. J. Pereira-Sáez 《Annals of Global Analysis and Geometry》2011,39(3):325-335
The aim of this article is to use the so-called Cayley transform in order to compute the LS category of Lie groups and homogeneous
spaces by giving explicit categorical open coverings. When applied to U(n), U(2n)/Sp(n) and U(n)/O(n) this method is simpler than those formerly known. We also show that the Cayley transform is related to height functions
in Lie groups, allowing to give a local linear model of the set of critical points. As an application we give an explicit
covering of Sp(2) by categorical open sets. The obstacles to generalize these results to Sp(n) are discussed. 相似文献
12.
Let 𝔽 be a field, V a 6-dimensional 𝔽-vector space and f a nondegenerate alternating bilinear form on V. We consider a 14-dimensional module for the symplectic group Sp(V, f) ? Sp(6, 𝔽) associated with (V, f), and classify the orbits on vectors. For characteristic distinct from 2, this module is irreducible and isomorphic to the Weyl module of Sp(V, f) for the fundamental weight λ3. If the characteristic is 2, then the module is reducible as it contains an 8-dimensional submodule isomorphic to the spin module of Sp(V, f). 相似文献
13.
Let P and Q be non-zero integers. The Lucas sequence {Un(P,Q)} is defined by U0=0, U1=1, Un=PUn−1−QUn−2 (n?2). The question of when Un(P,Q) can be a perfect square has generated interest in the literature. We show that for n=2,…,7, Un is a square for infinitely many pairs (P,Q) with gcd(P,Q)=1; further, for n=8,…,12, the only non-degenerate sequences where gcd(P,Q)=1 and Un(P,Q)=□, are given by U8(1,−4)=212, U8(4,−17)=6202, and U12(1,−1)=122. 相似文献
14.
Peter Köhler Thomas Meixner Michael Wester 《Journal of Combinatorial Theory, Series A》1985,38(2):203-209
A certain “free” group U is constructed that is generated by three elements of order 3 which pairwise generate a Frobenius group of order 21 and it is shown that U operates regularly on the affine building of type over the field of 2-adic numbers. As a result an infinite series of finite rank 3 geometries is obtained whose rank 2 residues are projective planes of order 2, and which possess a regular automorphism group isomorphic to SL3(p) or SU3(p) for some prime p. 相似文献
15.
A subgroup H of a group G is pronormal if the subgroups H and H g are conjugate in 〈H,H g 〉 for every g ∈ G. It was conjectured in [1] that a subgroup of a finite simple group having odd index is always pronormal. Recently the authors [2] verified this conjecture for all finite simple groups other than PSL n (q), PSU n (q), E 6(q), 2 E 6(q), where in all cases q is odd and n is not a power of 2, and P Sp2n (q), where q ≡ ±3 (mod 8). However in [3] the authors proved that when q ≡ ±3 (mod 8) and n ≡ 0 (mod 3), the simple symplectic group P Sp2n (q) has a nonpronormal subgroup of odd index, thereby refuted the conjecture on pronormality of subgroups of odd index in finite simple groups.The natural extension of this conjecture is the problem of classifying finite nonabelian simple groups in which every subgroup of odd index is pronormal. In this paper we continue to study this problem for the simple symplectic groups P Sp2n (q) with q ≡ ±3 (mod 8) (if the last condition is not satisfied, then subgroups of odd index are pronormal). We prove that whenever n is not of the form 2 m or 2 m (22k +1), this group has a nonpronormal subgroup of odd index. If n = 2 m , then we show that all subgroups of P Sp2n (q) of odd index are pronormal. The question of pronormality of subgroups of odd index in P Sp2n (q) is still open when n = 2 m (22k + 1) and q ≡ ±3 (mod 8). 相似文献
16.
Thomas H Pate 《Journal of Differential Equations》1979,34(2):261-272
If m and n are positive integers then let S(m, n) denote the linear space over R whose elements are the real-valued symmetric n-linear functions on Em with operations defined in the usual way. If is a function from some sphere S in Em to R then let (i)(x) denote the ith Frechet derivative of at x. In general (i)(x)∈S(m,i). In the paper “An Iterative Method for Solving Nonlinear Partial Differential Equations” [Advances in Math. 19 (1976), 245–265] Neuberger presents an iterative procedure for solving a partial differential equation of the form , where k > n, is the unknown from some sphere in Em to R, A is a linear functional on S(m, n), and F is analytic. The defect in the theory presented there was that in order to prove that the iterates converged to a solution the condition was needed. In this paper an iteration procedure that is a slight variation on Neuberger's procedure is considered. Although the condition cannot as yet be eliminated, it is shown that in a broad class of cases depending upon the nature of the functional A the restriction may be replaced by the restriction . 相似文献
17.
Manuel Amann 《Topology and its Applications》2011,158(2):183-189
Positive Quaternion Kähler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces. In this article we are mainly concerned with Positive Quaternion Kähler Manifolds M satisfying b4(M)=1. Generalising a result of Galicki and Salamon we prove that M4n in this case is homothetic to a quaternionic projective space if 2≠n?6. 相似文献
18.
Hiroaki Hamanaka 《Topology and its Applications》2007,154(3):573-583
The unitary group U(n) has elements εi∈π2i+1(U(n)) (0?i?n−1) of its homotopy groups in the stable range. In this paper we show that certain multi Samelson products of type 〈εi,〈εj,εk〉〉 are non-trivial. This leads us to the result that the nilpotency class of the group of the self homotopy set [SU(n),SU(n)] is no less than 3, if 4?n. Also by the power of generalized Samelson products, we can see the further result that, for a prime p and an integer n=pk, nil[SU(n),SU(n)](p)?3, if (1) p?7 or (2) p=5 and n≡0 or 1mod4. 相似文献
19.
J. Hu 《Transformation Groups》2010,15(2):333-370
Let V be a 2m-dimensional symplectic vector space over an algebraically closed field K. Let $ \mathfrak{B}_n^{(f)} Let V be a 2m-dimensional symplectic vector space over an algebraically closed field K. Let
\mathfrakBn(f) \mathfrak{B}_n^{(f)} be the two-sided ideal of the Brauer algebra
\mathfrakBn( - 2m ) {\mathfrak{B}_n}\left( { - 2m} \right) over K generated by e
1
e
3⋯
e
2f-1 where 0 ≤ f ≤ [n/2]. Let HTf ?n \mathcal{H}\mathcal{T}_f^{ \otimes n} be the subspace of partial-harmonic tensors of valence f in V
⊗n
. In this paper we prove that dimHTf ?n \mathcal{H}\mathcal{T}_f^{ \otimes n} and dim
\textEn\textdK\textSp(V)( V ?n \mathord