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1.
Henri Moscovici 《Israel Journal of Mathematics》1973,15(3):230-236
LetG be a Lie group,H a closed subgroup,L a unitary representation ofH andU
L the corresponding induced representation onG. The main result of this paper, extending Ol’ŝanskii’s version of the Frobenius reciprocity theorem, expresses the intertwining
number ofU
L and an irreducible unitary representationV ofG in terms ofL and the restriction ofV
∞ toH. 相似文献
2.
Michael Stiebitz 《Combinatorica》1982,2(3):315-323
Tibor Gallai made the following conjecture. LetG be ak-chromatic colour-critical graph. LetL denote the set of those vertices ofG having valencyk−1 and letH be the rest ofV(G). Then the number of components induced byL is not less than the number of components induced byH, providedL ≠ 0.
We prove this conjecture in a slightly generalized form.
Dedicated to Tibor Gallai on his seventieth birthday 相似文献
3.
LetG be a finite group and letR=Σ
g∈G
R
g
be any associative algebra over a field such that the subspacesR
g
satisfyR
g
R
h
⊆R
gh
. We prove that ifR
1 satisfies a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the order ofG. This result implies the following: ifH is a finite-dimensional semisimple commutative Hopfalgebra andR is anyH-module algebra withR
H
satisfying a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the dimension ofH. 相似文献
4.
Gordan Savin 《Israel Journal of Mathematics》1992,80(1-2):195-205
LetG andH ⊂G be two real semisimple groups defined overQ. Assume thatH is the group of points fixed by an involution ofG. Letπ ⊂L
2(H\G) be an irreducible representation ofG and letf επ be aK-finite function. Let Γ be an arithmetic subgroup ofG. The Poincaré seriesP
f(g)=ΣH∩ΓΓ
f(γ{}itg) is an automorphic form on Γ\G. We show thatP
f is cuspidal in some cases, whenH ∩Γ\H is compact.
Partially supported by NSF Grant # DMS 9103608. 相似文献
5.
LetM
2n,r
denote the vector space of real or complex2n×r matrices with the natural action of the symplectic group Sp
2n
, and letG=G
n,r
=Sp
2n
×M
2n,r
denote the corresponding semi-direct product. For any integerp with 0≤p≤n−1, letH denote the subgroupG
p,r
×Sp
2n−2p
ofG. We explicitly compute the algebra of left invariant differential operators onG/H, and we show that it is a free algebra if and only ifr≤2n−2p+1. We also give orthogonal analogues of these results, generalizing those of Gonzalez and Helgason [3].
Partially supported by NSF grant DMS-9101358
This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990. 相似文献
6.
Min Ho Lee 《manuscripta mathematica》1991,71(1):35-44
LetG⊃PSL(2,R) be a Fuchsian group of the first kind with no elements of finite order, and letS
2m
V be the 2m-fold symmetric power of the standard representationV ofSL(2,R) on C2. We determine the value of the Kronecker pairing between the canonical image of a mixed cusp formf of type (2,2m) inH
1(G, S
2m
V) and a cycleg ⊗Q
g
m
inH
1 (G, (S
2m
V)*) for eachg inG, whereQ
g
m
is an element of (S
2m
V)* associated tog, m and a monodromy representation ofG. 相似文献
7.
LetK be any field of characteristicp>0 and letG be a finite group acting onK via a map τ. The skew group algebraK
τG may be nonsemisimple (precisely whenP|(H), H=Kert). In [1] necessary conditions were given for the existence of a class α∈H
2(G,K*) which “twists” the skew group algebraK
τG into a semisimple crossed productK
τ
αG
. The “twisting problem” asks whether these conditions are sufficient. In [1] we showed that this is indeed so in many cases.
In this paper we prove it in general.
During the period of this research the second author was an Associate at the Center for Advanced Study, Urbana, Illinois. 相似文献
8.
William Kocay 《Graphs and Combinatorics》1992,8(3):259-276
LetV be a set ofn elements. The set of allk-subsets ofV is denoted
. Ak-hypergraph G consists of avertex-set V(G) and anedgeset
, wherek≥2. IfG is a 3-hypergraph, then the set of edges containing a given vertexvεV(G) define a graphG
v
. The graphs {G
v
νvεV(G)} aresubsumed byG. Each subsumed graphG
v
is a graph with vertex-setV(G) − v. They can form the set of vertex-deleted subgraphs of a graphH, that is, eachG
v
≽H −v, whereV(H)=V(G). In this case,G is a hypergraphic reconstruction ofH. We show that certain families of self-complementary graphsH can be reconstructed in this way by a hypergraphG, and thatG can be extended to a hypergraphG
*, all of whose subsumed graphs are isomorphic toH, whereG andG
* are self-complementary hypergraphs. In particular, the Paley graphs can be reconstructed in this way.
This work was supported by an operating grant from the Natural Sciences and Engineering Research Council of Canada. 相似文献
9.
LetG be a graph with vertex setV (G) and edge setE (G), and letg andf be two integer-valued functions defined on V(G) such thatg(x)⩽(x) for every vertexx ofV(G). It was conjectured that ifG is an (mg +m - 1,mf -m+1)-graph andH a subgraph ofG withm edges, thenG has a (g,f)-factorization orthogonal toH. This conjecture is proved affirmatively.
Project supported by the National Natural Science Foundation of China. 相似文献
10.
Leila Schneps 《Israel Journal of Mathematics》1996,93(1):125-144
LetG be a finite group of even order, having a central element of order 2 which we denote by −1. IfG is a 2-group, letG be a maximal subgroup ofG containing −1, otherwise letG be a 2-Sylow subgroup ofG. LetH=G/{±1} andH=G/{±1}. Suppose there exists a regular extensionL
1 of ℚ(T) with Galois groupG. LetL be the subfield ofL
1 fixed byH. We make the hypothesis thatL
1 admits a quadratic extensionL
2 which is Galois overL of Galois groupG. IfG is not a 2-group we show thatL
1 then admits a quadratic extension which is Galois over ℚ(T) of Galois groupG and which can be given explicitly in terms ofL
2. IfG is a 2-group, we show that there exists an element α ε ℚ(T) such thatL
1 admits a quadratic extension which is Galois over ℚ(T) of Galois groupG if and only if the cyclic algebra (L/ℚ(T).a) splits. As an application of these results we explicitly construct several 2-groups as Galois groups of regular extensions
of ℚ(T). 相似文献
11.
Barak Weiss 《Israel Journal of Mathematics》1998,106(1):189-207
LetH be an ℝ-subgroup of a ℚ-algebraic groupG. We study the connection between the dynamics of the subgroup action ofH onG/G
ℤ and the representation-theoretic properties ofH being observable and epimorphic inG. We show that ifH is a ℚ-subgroup thenH is observable inG if and only if a certainH orbit is closed inG/G
ℤ; that ifH is epimorphic inG then the action ofH onG/G
ℤ is minimal, and that the converse holds whenH is a ℚ-subgroup ofG; and that ifH is a ℚ-subgroup ofG then the closure of the orbit underH of the identity coset image inG/G
ℤ is the orbit of the same point under the observable envelope ofH inG. Thus in subgroup actions on homogeneous spaces, closures of ‘rational orbits’ (orbits in which everything which can be defined
over ℚ, is defined over ℚ) are always submanifolds. 相似文献
12.
L. Yu. Glebskii 《Mathematical Notes》1999,65(1):31-40
Theorems are proved establishing a relationship between the spectra of the linear operators of the formA+Ωg
iBigi
−1 andA+B
i, whereg
i∈G, andG is a group acting by linear isometric operators. It is assumed that the closed operatorsA andB
i possess the following property: ‖B
iA−1gBjA−1‖→0 asd(e,g)→∞. Hered is a left-invariant metric onG ande is the unit ofG. Moreover, the operatorA is invariant with respect to the action of the groupG. These theorems are applied to the proof of the existence of multicontour solutions of dynamical systems on lattices.
Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 37–47, January, 1999. 相似文献
13.
Guizhen LIU 《Frontiers of Mathematics in China》2009,4(2):311-323
Let G be a digraph with vertex set V(G) and arc set E(G) and let g = (g
−, g
+) and ƒ = (ƒ
−, ƒ
+) be pairs of positive integer-valued functions defined on V(G) such that g
−(x) ⩽ ƒ
−(x) and g
+(x) ⩽ ƒ
+(x) for each x ∈ V(G). A (g, ƒ)-factor of G is a spanning subdigraph H of G such that g
−(x) ⩽ id
H
(x) ⩽ ƒ
−(x) and g
+(x) ⩽ od
H
(x) ⩽ ƒ
+(x) for each x ∈ V(H); a (g, ƒ)-factorization of G is a partition of E(G) into arc-disjoint (g, ƒ)-factors. Let
= {F
1, F
2,…, F
m} and H be a factorization and a subdigraph of G, respectively.
is called k-orthogonal to H if each F
i
, 1 ⩽ i ⩽ m, has exactly k arcs in common with H. In this paper it is proved that every (mg+m−1,mƒ−m+1)-digraph has a (g, f)-factorization k-orthogonal to any given subdigraph with km arcs if k ⩽ min{g
−(x), g
+(x)} for any x ∈ V(G) and that every (mg, mf)-digraph has a (g, f)-factorization orthogonal to any given directed m-star if 0 ⩽ g(x) ⩽ f(x) for any x ∈ V(G). The results in this paper are in some sense best possible.
相似文献
14.
Given two hypergraphsH andG, letN(G, H) denote the number of subhypergraphs ofG isomorphic toH. LetN(l, H) denote the maximum ofN(G, H), taken over allG with exactlyl edges. In [1] Noga Alon analyzes the asymptotic behaviour ofN(l, H) forH a graph. We generalize this to hypergraphs:
Theorem:For a hypergraph H with fractional cover number ρ*,N(G,H).=θ(lρ*)
The interesting part of this is the upper bound, which is shown to be a simple consequence of an entropy lemma of J. Shearer.
In a special case which includes graphs, we also provide a different proof using a hypercontractive estimate.
Research supported in part by NSF. 相似文献
15.
Pravin M. Vaidya 《Discrete and Computational Geometry》1991,6(1):369-381
A setV ofn points ink-dimensional space induces a complete weighted undirected graph as follows. The points are the vertices of this graph and
the weight of an edge between any two points is the distance between the points under someL
p metric. Let ε≤1 be an error parameter and letk be fixed. We show how to extract inO(n logn+ε
−k
log(1/ε)n) time a sparse subgraphG=(V, E) of the complete graph onV such that: (a) for any two pointsx, y inV, the length of the shortest path inG betweenx andy is at most (1+∈) times the distance betweenx andy, and (b)|E|=O(ε−k
n). 相似文献
16.
LetG be a group,ZG the integral group ring ofG andI(G) its augmentation ideal. Subgroups determined by certain ideals ofZG contained inI(G) are identified. For example, whenG=HK, whereH, K are normal subgroups ofG andH∩K⊆ζ(H), then the subgroups ofG determined byI(G)I(H)I(G), andI
3(G)I(H) are obtained. The subgroups of any groupG with normal subgroupH determined by (i)I
2(G)I(H)+I(G)I(H)I(G)+I(H)I2(G), whenH′⊆[H,G,G] and (ii)I(G)I(H)I(G) when degH
2(G/H′, T)≤1, are computed. the subgroup ofG determined byI
n(G)+I(G)I(H) whenH is a normal subgroup ofG withG/H free Abelian is also obtained 相似文献
17.
Letp be a prime,K a field of characteristicp, G a locally finitep-group,KG the group algebra, andV the group of the units ofKG with augmentation 1. The anti-automorphismg→g
−1 ofG extends linearly toKG; this extension leavesV setwise invariant, and its restriction toV followed byv→v
−1 gives an automorphism ofV. The elements ofV fixed by this automorphism are calledunitary; they form a subgroup. Our first theorem describes theK andG for which this subgroup is normal inV.
For each elementg inG, let
denote the sum (inKG) of the distinct powers ofg. The elements 1+(g-1)
withh,hεG are thebicyclic units ofKG. Our second theorem describes theK andG for which all bicyclic units are unitary.
Research partly supported by the Hungarian National Foundation for Scientific Research grant no. T4265.
The second author is indebted to the ‘Universitas’ Foundation and the Lajos Kossuth University of Debrecen, Hungary, for warm
hospitality and generous support during the period when this work began.
This article was processed by the authors using the Springer-Verlag TEX mamath macro package 1990. 相似文献
18.
George T. Diderrich 《Israel Journal of Mathematics》1973,14(1):14-22
LetG be an Abelian group written additively,B a finite subset ofG, and lett be a positive integer. Fort≦|B|, letB
t denote the set of sums oft distinct elements overB. Furthermore, letK be a subgroup ofG and let σ denote the canonical homomorphism σ:G→G/K. WriteB
t (modB
t) forB
tσ and writeB
t (modK) forBσ. The following addition theorem in groups is proved. LetG be an Abelian group with no 2-torsion and letB a be finite subset ofG. Ift is a positive integer such thatt<|B| then |B
t (modK)|≧|B (modK)| for any finite subgroupK ofG. 相似文献
19.
Dmitri N. Akhiezer 《manuscripta mathematica》1993,80(1):81-88
LetG be a connected, reductive, linear algebraic group over an algebraically closed fieldk of characteristik zero. LetH 1 andH 2 be two spherical subgroups ofG. It is shown that for allg in a Zariski open subset ofG one has a Lie algebra decomposition g = h1 + Adg ? h2, where a is the Lie algebra of a torus and dim a ≤ min (rankG/H 1,rankG/H 2). As an application one obtains an estimate of the transcendence degree of the fieldk(G/H 1 xG/H 2) G for the diagonal action ofG. Ifk = ? andG a is a real form ofG defined by an antiholomorphic involution σ :G→G then for a spherical subgroup H ? G and for allg in a Hausdorff open subset ofG one has a decomposition g = ga + a Adg ? h, where a is the Lie algebra of σ-invariant torus and dim a ≤ rankG/H. 相似文献
20.
E. Ballico 《Annali dell'Universita di Ferrara》1999,45(1):123-125
Fix integersg, k andt witht>0,k≥3 andtk<g/2−1. LetX be a generalk-gonal curve of genusg andR∈Pic
k
(X) the uniqueg
k
1
onX. SetL:=K
X⊗(R
*)⊗t.L is very ample. Leth
L:X→P(H
0(X, L)*) be the associated embedding. Here we prove thath
L(X) is projectively normal. Ifk≥4 andtk<g/2−2 the curveh
L(X) is scheme-theoretically cut out by quadrics.
The author was partially supported by MURST and GNSAGA of CNR (Italy). 相似文献