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1.
In this article we determine the irreducible ordinary characters cr \chi_r of a finite group G occurring in a transitive permutation representation (1M )G of a given subgroup M of G, and their multiplicities mr = ((1M)G, cr) 1 0 m_r = ((1_{M})^G, \chi_r) \neq 0 by means of a new explicit formula calculating the coefficients ark of the central idempotents er = ?k=1d ark Dk e_r = \sum\limits_{k=1}^{d} a_{rk} D_k in the intersection algebra B \cal B of (1M )G generated by the intersection matrices Dk corresponding to the double coset decomposition G = èk=1d Mxk M G = \bigcup\limits_{k=1}^{d} Mx_{k} M .¶Furthermore, an explicit formula is given for the calculation of the character values cr(x) \chi_{r}(x) of each element x ? G x \in G . Using this character formula we obtain a new practical algorithm for the calculation of a substantial part of the character table of G. 相似文献
2.
W. Müller 《Geometric And Functional Analysis》2000,10(5):1118-1170
Let G be a reductive algebraic group defined over \Bbb Q {\Bbb Q} . Let P, P' be parabolic subgroups of G, defined over \Bbb Q {\Bbb Q} , and let _boxclose_boxclose, a_P') t \in W({\frak a}_{P}, {\frak a}_{P'}) . In this paper we study the intertwining operator MP¢|P(t,l), l ? \frak a*P,\Bbb C M_{P' \vert P}(t,\lambda),\,\lambda \in {\frak a}^*_{P,{\Bbb C}} , acting in corresponding spaces of automorphic forms. One of the main results states that each matrix coefficient of MP¢|P(t,l) M_{P' \vert P}(t,\lambda) is a meromorphic function of order £ n + 1 \le n + 1 , where n = dim G. Using this result, we further investigate the rank one intertwining operators, in particular, we study the distribution of their poles. 相似文献
3.
Alireza Abdollahi 《Archiv der Mathematik》1999,73(2):104-108
In this note we prove that every infinite group G is 3-abelian (i.e. (ab)3 = a3b3 for all a, b in G) if and only if in every two infinite subsets X and Y of G there exist x ? Xx\in X and y ? Yy\in Y such that (xy)3 = x3y3. 相似文献
4.
G. Kutyniok 《Archiv der Mathematik》2002,78(2):135-144
Let
r\mathbbR \rho_{\mathbb{R}} be the classical Schrödinger representation of the Heisenberg group and let L \Lambda be a finite subset of
\mathbbR ×\mathbbR \mathbb{R} \times \mathbb{R} . The question of when the set of functions
{t ? e2 pi y t f(t + x) = (r\mathbbR(x, y, 1) f)(t) : (x, y) ? L} \{t \mapsto e^{2 \pi i y t} f(t + x) = (\rho_{\mathbb{R}}(x, y, 1) f)(t) : (x, y) \in \Lambda\} is linearly independent for all
f ? L2(\mathbbR), f 1 0 f \in L^2(\mathbb{R}), f \neq 0 , arises from Gabor analysis. We investigate an analogous problem for locally compact abelian groups G. For a finite subset L \Lambda of G ×[^(G)] G \times \widehat{G} and rG \rho_G the Schrödinger representation of the Heisenberg group associated with G, we give a necessary and in many situations also sufficient condition for the set {rG (x, w, 1)f : (x, w) ? L} \{\rho_G (x, w, 1)f : (x, w) \in \Lambda\} to be linearly independent for all f ? L2(G), f 1 0 f \in L^2(G), f \neq 0 . 相似文献
5.
Arturo Magidin 《Algebra Universalis》2002,48(2):145-150
We characterize when a subgroup H of a group G is epimorphically embedded in G in a varietal product NQ \mathcal{NQ} , in terms of the epimorphisms in N \mathcal{N} and the laws of Q \mathcal{Q} . This reduces the characterization of nonsurjective epimorphisms to the indecomposable varieties. We also prove that the existence of an epimorphically embedded proper subgroup of a simple group in N \mathcal{N} implies the existence of a nonsurjective epimorphism in any varietal product NQ \mathcal{NQ} , provided that Q \mathcal{Q} is not the variety of all groups. 相似文献
6.
Suppose G is a transitive permutation group on a finite set W\mit\Omega of n points and let p be a prime divisor of |G||G|. The smallest number of points moved by a non-identity p-element is called the minimal p-degree of G and is denoted mp (G). ¶ In the article the minimal p-degrees of various 2-transitive permutation groups are calculated. Using the classification of finite 2-transitive permutation groups these results yield the main theorem, that mp(G) 3 [(p-1)/(p+1)] ·|W|m_{p}(G) \geq {{p-1} \over {p+1}} \cdot |\mit\Omega | holds, if Alt(W) \nleqq G {\rm Alt}(\mit\Omega ) \nleqq G .¶Also all groups G (and prime divisors p of |G||G|) for which mp(G) £ [(p-1)/(p)] ·|W|m_{p}(G)\le {{p-1}\over{p}} \cdot |\mit\Omega | are identified. 相似文献
7.
We factor the virtual Poincaré polynomial of every homogeneous space G/H, where G is a complex connected linear algebraic group and H is an algebraic subgroup, as t2u (t2–1)r QG/H(t2) for a polynomial QG/H with nonnegative integer coefficients. Moreover, we show that QG/H(t2) divides the virtual Poincaré polynomial of every regular embedding of G/H, if H is connected. 相似文献
8.
S. Haruki 《Aequationes Mathematicae》2002,63(3):201-209
Summary. Let (G, +) and (H, +) be abelian groups such that the equation 2u = v 2u = v is solvable in both G and H. It is shown that if f1, f2, f3, f4, : G ×G ? H f_1, f_2, f_3, f_4, : G \times G \longrightarrow H satisfy the functional equation f1(x + t, y + s) + f2(x - t, y - s) = f3(x + s, y - t) + f4(x - s, y + t) for all x, y, s, t ? G x, y, s, t \in G , then f1, f2, f3, and f4 are given by f1 = w + h, f2 = w - h, f3 = w + k, f4 = w - k where w : G ×G ? H w : G \times G \longrightarrow H is an arbitrary solution of f (x + t, y + s) + f (x - t, y - s) = f (x + s, y - t) + f (x - s, y + t) for all x, y, s, t ? G x, y, s, t \in G , and h, k : G ×G ? H h, k : G \times G \longrightarrow H are arbitrary solutions of Dy,t3g(x,y) = 0 \Delta_{y,t}^{3}g(x,y) = 0 and Dx,t3g(x,y) = 0 \Delta_{x,t}^{3}g(x,y) = 0 for all x, y, s, t ? G x, y, s, t \in G . 相似文献
9.
In this paper it will be shown that any two \bf\cal V-covering groups of a given group are V\bf\cal V-isologic with respect to the variety V\bf\cal V, which is a vast generalization of a result in B. Huppert (1967) and R. L. Griess JR (1973). We also give a criterion of existence of V\bf\cal V-covering groups for a V\bf\cal V-perfect group, and show that every automorphism of a given V\bf\cal V-perfect group G can be extended to an automorphism of the V\bf\cal V-covering G* say, of G, this generalizes a result of J. L. Alperin and D. Gorenstein (1966), in the abelian variety. 相似文献
10.
I. Corovei 《Aequationes Mathematicae》2001,61(3):212-220
Summary. Consider Wilson's functional equation¶¶f(xy) + f(xy-1) = 2f(f)g(y) f(xy) + f(xy^{-1}) = 2f(f)g(y) , for f,g : G ? K f,g : G \to K ¶where G is a group and K a field with char K 1 2 {\rm char}\, K\ne 2 .¶Aczél, Chung and Ng in 1989 have solved Wilson's equation, assuming that the function g satisfies Kannappan's condition g(xyz) = g(xzy) and f(xy) = f(yx) for all x,y,z ? G x,y,z\in G .¶In the present paper we obtain the general solution of Wilson's equation when G is a P3-group and we show that there exist solutions different of those obtained by Aczél, Chung and Ng.¶A group G is said to be a P3-group if the commutator subgroup G' of G, generated by all commutators [x,y] := x-1y-1xy, has the order one or two. 相似文献
11.
The Euler monoid En = {(a,b,t) epsilon Z3 : a2 + b2 = tn, n S 1, is free if and only if n is odd (Theorem 1). We extend the results of Lyndon and Ullman, and Beardon concerning the set of those rational numbers mu epsilon (-2,2) for which the matrix Möbius group Gmu generated by A= and B = is not free (Theorems 2, 3, 4). 相似文献
12.
Straightening and bounded cohomology of hyperbolic groups 总被引:2,自引:0,他引:2
I. Mineyev 《Geometric And Functional Analysis》2001,11(4):807-839
It was stated by M. Gromov [Gr2] that, for any hyperbolic group G, the map from bounded cohomology Hnb(G,\Bbb R) H^n_b(G,{\Bbb R}) to Hn(G,\Bbb R) H^n(G,{\Bbb R}) induced by inclusion is surjective for n 3 2 n \ge 2 . We introduce a homological analogue of straightening simplices, which works for any hyperbolic group. This implies that the map Hnb(G,V) ? Hn(G,V) H^n_b(G,V) \to H^n(G,V) is surjective for n 3 2 n \ge 2 when V is any bounded \Bbb QG {\Bbb Q}G -module and when V is any finitely generated abelian group. 相似文献
13.
M. I. Hartley 《Aequationes Mathematicae》1999,57(1):108-120
Summary. In an earlier paper, it was shown that every abstract polytope is a quotient Q = M(W)/N {\cal Q} = {\cal M}(W)/N of some regular polytope M(W) {\cal M}(W) whose automorphism group is W, by a subgroup N of W. In this paper, attention is focussed on the quotient Q {\cal Q} , and various important structures relating to polytopes are described in terms of N ', the stabilizer of a flag of the quotient under an action of W (the 'flag action'). It is pointed out how N ' may be assumed without loss of generality to equal N. The paper also shows what properties of N ' yield polytopes which are regular, section regular, chiral, locally regular, or locally universal. The aim is to make it more practical to study non-regular polytopes in terms of group theory. 相似文献
14.
S. Kawata 《Archiv der Mathematik》2000,75(2):92-97
Let G be a finite group and O{\cal O} a complete discrete valuation ring of characteristic zero with maximal ideal (p)(\pi ) and residue field k = O/(p)k = {\cal O}/(\pi ) of characteristic p > 0. Let S be a simple kG-module and QS a projective O G{\cal O} G-lattice such that QS / pQSQ_S / \pi Q_S is a projective cover of S. We show that if S is liftable and QS belongs to a block of O G{\cal O} G of infinite representation type, then the standard Auslander-Reiten sequence terminating in W-1S\Omega ^{-1}S is a direct summand of the short exact sequence obtained from some Auslander-Reiten sequence of OG{\cal O}G-lattices by reducing each term mod (p)(\pi ). 相似文献
15.
G. Turowski 《Archiv der Mathematik》2001,77(3):278-288
This paper is the second part of our investigations on doubly connected minimal surfaces which are stationary in a boundary configuration (G, S) (\Gamma, S) in \Bbb R 3 \Bbb R ^3 . The support surface S is a vertical cylinder above a simple closed polygon P(S) P(S) in the x,y-plane. The surrounding Jordan curve G \Gamma is chosen as a generalized graph above its convex projection curve P(G) P(\Gamma) . In [23] we have proved the existence of nonparametric minimal surfaces X of annulus type spanning such boundary configurations. We study the behaviour of these minimal surfaces at the edges of the support surface S. In particular we discuss the phenomenon of edge-creeping, i. e. the fact that the free trace of X may attach to an edge of S in a full interval. We prove that a solution X cuts any intruding edge of S perpendicularly. On the other hand, we derive a condition which forces X to exhibit the edge-creeping behaviour. Depending on the symmetries of (G, S) (\Gamma, S) we give bounds on the number of edges where edge-creeping occurs. Let (x,y,Z (x,y)) (x,y,\hbox {Z} (x,y)) for (x,y) ? G (x,y)\in G be the nonparametric representation of X. Then at every vertex Q of P(S) P(S) the radial limits of Z from all directions in G exist. 相似文献
16.
Rolf Farnsteiner 《Archiv der Mathematik》1999,72(1):28-39
Let (L,[p]) a finite dimensional nilpotent restricted Lie algebra of characteristic p 3 3, c ? L*p \geq 3, \chi \in L^* a linear form. In this paper we study the representation theory of the reduced universal enveloping algebra u(L,c)u(L,\chi ). It is shown that u(L,c)u(L,\chi ) does not admit blocks of tame representation type. As an application, we prove that the nonregular AR-components of u(L,c)u(L,\chi ) are of types \Bbb Z [A¥ ]\Bbb Z [A_\infty ] or \Bbb Z [An]/(t)\Bbb Z [A_n]/(\tau ). 相似文献
17.
R.J. McCann 《Geometric And Functional Analysis》2001,11(3):589-608
Let (M,g) be a connected compact manifold, C3 smooth and without boundary, equipped with a Riemannian distance d(x,y). If s : M ? M s : M \to M is merely Borel and never maps positive volume into zero volume, we show s = t °u s = t \circ u factors uniquely a.e. into the composition of a map t(x) = expx[-?y(x)] t(x) = {\rm exp}_x[-\nabla\psi(x)] and a volume-preserving map u : M ? M u : M \to M , where y: M ? \bold R \psi : M \to {\bold R} satisfies the additional property that (yc)c = y (\psi^c)^c = \psi with yc(y) :=inf{c(x,y) - y(x) | x ? M} \psi^c(y) :={\rm inf}\{c(x,y) - \psi(x)\,\vert\,x \in M\} and c(x,y) = d2(x,y)/2. Like the factorization it generalizes from Euclidean space, this non-linear decomposition can be linearized around the identity to yield the Hodge decomposition of vector fields.¶The results are obtained by solving a Riemannian version of the Monge--Kantorovich problem, which means minimizing the expected value of the cost c(x,y) for transporting one distribution f 3 0 f \ge 0 of mass in L1(M) onto another. Parallel results for other strictly convex cost functions c(x,y) 3 0 c(x,y) \ge 0 of the Riemannian distance on non-compact manifolds are briefly discussed. 相似文献
18.
V.G. Pestov 《Geometric And Functional Analysis》2000,10(5):1171-1201
We establish a close link between the amenability property of a unitary representation p \pi of a group G (in the sense of Bekka) and the concentration property (in the sense of V. Milman) of the corresponding dynamical system (\Bbb Sp, G) ({\Bbb S}_{\pi}, G) , where \Bbb SH {\Bbb S}_{\cal H} is the unit sphere the Hilbert space of representation. We prove that p \pi is amenable if and only if either p \pi contains a finite-dimensional subrepresentation or the maximal uniform compactification of (\Bbb Sp ({\Bbb S}_{\pi} has a G-fixed point. Equivalently, the latter means that the G-space (\Bbb Sp, G) ({\Bbb S}_{\pi}, G) has the concentration property: every finite cover of the sphere \Bbb Sp {\Bbb S}_{\pi} contains a set A such that for every e > 0 \epsilon > 0 the e \epsilon -neighbourhoods of the translations of A by finitely many elements of G always intersect. As a corollary, amenability of p \pi is equivalent to the existence of a G-invariant mean on the uniformly continuous bounded functions on \Bbb Sp {\Bbb S}_{\pi} . As another corollary, a locally compact group G is amenable if and only if for every strongly continuous unitary representation of G in an infinite-dimensional Hilbert space H {\cal H} the system (\Bbb SH, G) ({\Bbb S}_{\cal H}, G) has the property of concentration. 相似文献
19.
S. Dolfi 《Archiv der Mathematik》2000,75(5):321-327
Let G be a permutation group on a finite set W\Omega . If G does not involve An for n \geqq 5 n \geqq 5 , then there exist two disjoint subsets of W\Omega such that no Sylow subgroup of G stabilizes both and four disjoint subsets of W\Omega whose stabilizers in G intersect trivially. 相似文献
20.
The main aim of this paper is to obtain a dual result to the now well known Auslander-Bridger formula for G-dimension. We will show that if R is a complete Cohen-Macaulay ring with residue field k, and M is a non-injective h-divisible Ext-finite R-module of finite Gorenstein injective dimension such that for each i 3 1i \geq 1 Exti (E,M) = 0 for all indecomposable injective R-modules E 1 E(k)E \neq E(k), then the depth of the ring is equal to the sum of the Gorenstein injective dimension and Tor-depth of M. As a consequence, we get that this formula holds over a d-dimensional Gorenstein local ring for every nonzero cosyzygy of a finitely generated R-module and thus in particular each such nth cosyzygy has its Tor-depth equal to the depth of the ring whenever n 3 dn \geq d. 相似文献