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We express them in terms of generatorsEij ofU(gl(n)) and as differential operators on the space of matrices These expressions are a direct generalization of the classical Capelli identities.
      
In particular, we give a detailed description of these sets in terms of cross-sections inside maximal R-tori ofH.
      
A characterization of the complexity of a homogeneous space of a reductive groupG is given in terms of the mutual position of the tangent Lie algebra of the stabilizer of a generic point of and the (-1)-eigenspace of a Weyl involution of.
      
Indeed, we will give a full classification of the manifoldsN(g, V) which are commutative spaces, using a characterization in terms of multiplicity-free actions.
      
It was then observed independentely by Lusztig and Ginzburg-Vasserot (see [L1], [GV]) that this construction admits an affine analogue in terms of periodic flags of lattices.
      
These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of levelk.
      
In this paper we give a characterization of symmetric Siegel domains in terms of a certain norm equality which involves a Cayley transform.
      
We give a lower bound for the values Px,w(1) in terms of "patterns".
      
We find closed formulas for the 1-point functions in both cases in terms of Jacobi θ-functions.
      
As the third application, we describe a K-basis for the ring of invariants for the adjoint action of ${\rm SL}_2(K)$ on m copies of $sl_2(K)$ in terms of traces.
      
We characterize irreducible Hermitian symmetric spaces which are not of tube type, both in terms of
      
When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form.
      
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.
      
We study nonlinear dispersive systems of the form where k=1, …, n, j ∈ ?+, and Pk(·) are polynomials having no constant or linear terms.
      
In Section 2 of this article, we characterize stability and linear independence of the shifts of a finite refinable function set in terms of the refinement mask.
      
First, a projectively invariant classification of patterns is constructed in terms of orbits of the groupPSL(2, ?) acting on the image plane (with complex coordinates) by linear-fractional transformations.
      
The admissibility conditions for the wavelet measure μ are presented in terms of μ itself and in terms of the Fourier transform of μ.
      
The supports of functions are described in terms of their modified Mellin (or inverse Mellin) transform without passing to the complexification.
      
We prove the well-posedness when and construct non-unique solutions for In the second part the well-posedness of the avove IVP for k=2 with μ0?Hs(?n) is proved if and this result is then extended for more general nonlinear terms and initial data.
      
In this paper, we clarify exactly how "bad" such Gabor expansions are, we make it clear precisely where the edge is between "enough" and "too little," and we find a remedy for their shortcomings in terms of a certain summability method.
      
 

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