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1.
We construct quantum deformations of imaginary Verma modulesover and show that, for generic q, imaginary Verma modules over can be deformed to those over the quantum group in such a way that the dimensions of the weightspaces are invariant under the deformation. We also prove thePBW theorem for with respect to the triangular decomposition induced from the root partitioncorresponding to the imaginary Verma modules. 1991 MathematicsSubject Classification: 17B67, 17B65, 17B10.  相似文献   

2.
Let G be a graph of order 2n + l having maximum degree 2n –1. We prove that the total chromatic number of G is 2n if andonly if e + ' n, where w is a vertex of minimum degree in G, is the complement of Gw, e is the size of , and ' is the edge independence number of .  相似文献   

3.
Let V be a complete connected hyperbolic 3-manifold of finitevolume, with Liouville measure m, geodesic flow t and Brownianmotion Zt. Let be a smooth 1-form, closed in the cusps of V.Then the limit laws as t of under m and of are calculated, and seen to be Gaussian, and equal. The geodesic flow case isstudied via the Brownian case. 1991 Mathematics Subject Classification:60J65, 58F17, 51M10.  相似文献   

4.
Consider the group scheme where R is an arbitrary commutative ring with 1 0 and a unitx R* acts on R by multiplication. We will study the finiteness properties of subgroups of G(OS)where OS is an S-arithmetic subring of a global function field.The subgroups we are interested in are of the form where Q is a subgroup of OS*. The finiteness propertiesof these metabelian groups can be expressed in terms of the-invariant due to R. Bieri and R. Strebel. Theorem A. Let S be a finite set of places of a global functionfield (regarded as normalized discrete valuations) and OS thecorresponding S-arithmetic ring. Let Q be a subgroup of OS*.Then Q is finitely generated and for all integers n 1 the followingare equivalent:
(1) OS Q is of type FPn;
(2) OS is n-tameas a ZQ-module;
(3) each p S restricts to a non-trivial homomorphism and the set is n-tame.
If these conditions hold for at least one n 1 then the identity holds.} Theorem B. Let r denote the rank of Q. Then the followinghold:
(1) the group OS Q is not of type FPr+1};
(2) if Qhas maximum rank r = |S| –1 then the group OS Q is oftype FPr.
In particular, is of type FP|S| –1 but not of type FP|S|. 1991 Mathematics SubjectClassification: 20E08, 20F16, 20G30, 52A20.  相似文献   

5.
Let S(x,y) be the set S(x,y)= 1 n x : P(n) y, where P(n) denotesthe largest prime factor of n. We study , where f is a multiplicative function. When f=1and when f=µ, we widen the domain of uniform approximationusing the method of Fouvry and Tenenbaum and making explicitthe contribution of the Siegel zero. Soit S(x,y) l'ensemble S(x,y)= 1 n x : P(n) y, désigne le plus grand facteur premier den. Nous étudions , lorsque f est une fonction multiplicative. Quand f=1 et quand f=µ,nous élargissons le domaine d'approximation uniformeenutilisant la méthode développée par Fouvryet Tenenbaum et en explicitant la contribution du zérode Siegel. 1991 Mathematics Subject Classification: 11N25, 11N99.  相似文献   

6.
Let an be an increasing sequence of positive reals with an as n . Necessary and sufficient conditions are obtained foreach of the sequences to take on infinitely many prime values for almost all > rß.For example, the sequence an is infinitely often prime for almostall > 0 if and only if there is a subsequence of the an,say bn, with bn + 1 > bn + 1 and with the series divergent. Asymptotic formulae areobtained when the sequences considered are lacunary. An earlierresult of the author reduces the problem to estimating the measureof overlaps of certain sets, and sieve methods are used to obtainthe correct order upper bounds. 1991 Mathematics Subject Classification:primary 11N05; secondary 11K99, 11N36.  相似文献   

7.
A Mackey functor M is a structure analogous to the representationring functor H R(H) encoding good formal behaviour under inductionand restriction. More explicitly, M associates an abelian groupM(H) to each closed subgroup H of a fixed compact Lie groupG, and to each inclusion K H it associates a restriction map and an induction map . This paper gives an analysis of thecategory of Mackey functors M whose values are rational vectorspaces: such a Mackey functor may be specified by giving a suitablycontinuous family consisting of a Q 0(WG(H))-module V(H) foreach closed subgroup H with restriction maps V(K) V(K) wheneverK is normal in K and K/K is a torus (a ‘continuous Weyl-toralmodule’). We show that the category of rational Mackeyfunctors is equivalent to the category of rational continuousWeyl-toral modules. In Part II this will be used to give analgebraic analysis of the category of rational Mackey functors,showing in particular that it has homological dimension equalto the rank of the group. 1991 Mathematics Subject Classification:19A22, 20C99, 22E15, 55N91, 55P42, 55P91.  相似文献   

8.
Weak Covering Properties of Weak Topologies   总被引:1,自引:0,他引:1  
We consider covering properties of weak topologies of Banachspaces, especially of weak or point-wise topologies of functionspaces C(K), for compact spaces K. We answer questions posedby A. V. Arkhangel'skii, S. P. Gul'ko, and R. W. Hansell. Ourmain results are the following. A Banach space of density atmost 1 is hereditarily metaLindel of in its weak topology. Ifthe weight of a compact spaceK is at most 1, then the spacesCw(K) and Cp(K) are hereditarily metaLindel of. Let be the one-point compactificationof a treeT. Then the space is hereditarily -metacompact. If T is an infinitely branchingfull tree of uncountable height and of cardinality bigger thanc, then the weak topology of the unit sphere of is not -fragmented by any metric. The space Cp(rß1)is neither metaLindel of nor -relatively metacompact. The spaceCp(rß2) is not -relatively metaLindel of. Under theset-theoretic axiom , there exists a scattered compact spaceK1 such that the space Cp(K1) is not -relatively metacompact,and under a related axiom , there exists a scattere compactspace K2 such that the space Cp(K2) is not -relatively metaLindelof. 1991 Mathematics Subject Classification: 54C35, 46B20, 54E20,54D30.  相似文献   

9.
The Novikov-Landweber algebra and the Steenrod algebra are setup in terms of the primitive differential operators acting in the usual way on the integralpolynomial ring Z[x1,... ,xn,...]. A commutative wedge productV for differential operators is introduced and it is shown thatthe iterated wedge product is divisible by r! as an integral operator. The divided differentialoperator algebra D is generated over the integers by thedividedoperators under the wedge product. D is additively isomorphic to the abelian group ofsymmetric functions in the variables xi. Furthermore D is closedunder composition of operators and admits a natural coproductwhich makes it a Hopf algebra in two ways, with respect to thecomposition and wedge products. Under composition D is isomorphicto the Landweber-Novikov algebra. A Hopf sub-algebra is generatedunder composition by the integral Steenrod squares and reduces mod 2 to the Steenrod algebra. An explicitproduct formula for two wedge expressions is developed and usedto derive Milnor's product formula for his basis elements inthe Steenrod algebra. The hit problem in the Steenrod algebrais reformulated in terms of partial differential operators.1991 Mathematics Subject Classification: 55S10.  相似文献   

10.
Generalized compound quadrature formulae for finite-part integrals   总被引:1,自引:0,他引:1  
Received on 31 July 1995. Revised on 19 August 1996. We investigate the error term of the dth degree compound quadratureformulae for finite-part integrals of the form where and p 1.We are mainly interested in error bounds of the form with best possible constants c. Itis shown that, for and n uniformlydistributed nodes, the error behaves as O(np–s–1for , p–1 <s d+1.In a previous paper we have shown that this is not true for As an improvement, we consider the case of non-uniformly distributednodes. Here, we show that for all p I and , an O(ns) error estimate can be obtainedin theory by a suitable choice of the nodes. A set of nodeswith this property is staled explicitly. In practice, this gradedmesh causes stability problems which are computationally expensiveto overcome. E-mail address: diethelm{at}informatik.uni-hildesheim.de  相似文献   

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