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 properties They result in many nontrivial properties of quantum immanants. The paper studies generic commutative and anticommutative algebras of a fixed dimension, their invariants, covariants and algebraic properties (e.g., the structure of subalgebras). Whenever the action of a maximal torus on the coneCλ* has some nice properties, we obtain simple closed formulas for all weight multiplicities and theirq-analogs in the representationsVnλ,n∈?. Some basic properties of the compactness propertiesCn are shown. A local-global principle for finiteness properties ofS-arithmetic groups over number fields This paper introduces the concept ofn-valued groups and studies their algebraic and topological properties. Using the properties ofn-Hopf algebras we show that certain spaces do not admit the structure of ann-valued group and that certain commutativen-valued groups do not arise by applying then-coset construction to any commutative group. the volume computations involve several different methods according to the parity of dimension, subgroup relations and arithmeticity properties. The first part of this paper describes the construction of pseudo-Riemannian homogeneous spaces with special curvature properties such as Einstein spaces, using corresponding known compact Riemannian ones. We study their general properties and apply these results to Schubert varieties. Symmetry properties and cocycle properties of the Maslov index are then easily obtained. We then show that there is a unique order-reversing duality map No,c → LNo,c that has certain properties analogous to those of the original Lusztig-Spaltenstein duality map. The theory of PBW properties of quadratic algebras, to which this Such properties are expressed using the Furstenberg boundary of the associated symmetric space ? × ?. In the process we study the properties of different homogeneous models for ${\mathbb H}H(n).$ The main theme of this paper is that many of the remarkable properties of invariant theory pertaining to semisimple Lie algebras carry over to parabolic subalgebras even though the latter have less structure. We show that several properties of the semisimple algebras carry over to a certain family of parabolic subalgebras of maximal index in sln. In this paper we introduce, and study some basic properties of, the algebra of reciprocal polynomials A(V). This paper presents an expansion for radial tempered distributions on ${\bf R}^n$ in terms of smooth, radial analyzing and synthesizing functions with space-frequency localization properties similar to standard wavelets. It was recently observed that the behavior of a lattice $(m \alpha , n \beta )$ can be connected to that of a dual lattice $(m/ \beta , n /\alpha ).$ Here we establish this interesting relationship and study its properties.

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2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社