共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we prove a combinatorial rule describing the restriction of any irreducible representation of U(n+m) to the subgroup U(n)×U(m). We also derive similar rules for the reductions from SU(n+m) to S(U(n)×U(m)), and from SU(n+m) to SU(n)×SU(m). As applications of these representation-theoretic results, we compute the spectra of the Bochner–Laplacian on powers of the determinant bundle over the complex Grassmannian . The spectrum of the Dirac operator acting on the spin Grassmannian is also partially computed. A further application is given by the determination of the spectrum of the Hodge–Laplacian acting on the space of smooth functions on the unit determinant bundle over . 相似文献
2.
Leonid Gurvits 《Advances in Mathematics》2006,200(2):435-454
We prove that the mixed discriminant of doubly stochastic n-tuples of semidefinite hermitian n×n matrices is bounded below by and that this bound is uniquely attained at the n-tuple . This result settles a conjecture posed by R. Bapat in 1989. We consider various generalizations and applications of this result. 相似文献
3.
Seok-Zun Song Kyung-Tae Kang LeRoy B. Beasley Nung-Sing Sze 《Linear algebra and its applications》2008,429(1):209-223
An m×n matrix A over a semiring is called regular if there is an n×m matrix G over such that AGA=A. We study the problem of characterizing those linear operators T on the matrices over a semiring such that T(X) is regular if and only if X is. Complete characterizations are obtained for many semirings including the Boolean algebra, the nonnegative reals, the nonnegative integers and the fuzzy scalars. 相似文献
4.
An n-lift of a graph K is a graph with vertex set V(K)×[n], and for each edge (i,j)E(K) there is a perfect matching between {i}×[n] and {j}×[n]. If these matchings are chosen independently and uniformly at random then we say that we have a random n-lift. We show that there are constants h1,h2 such that if h≥h1 then a random n-lift of the complete graph Kh is hamiltonian and if h≥h2 then a random n-lift of the complete bipartite graph Kh,h is hamiltonian . 相似文献
5.
In this paper we investigate the L2-solutions of vector refinement equations with exponentially decaying masks and a general dilation matrix. A vector refinement equation with a general dilation matrix and exponentially decaying masks is of the formwhere the vector of functions φ=(φ1,…,φr)T is in is an exponentially decaying sequence of r×r matrices called refinement mask and M is an s×s integer matrix such that limn→∞M-n=0. Associated with the mask a and dilation matrix M is a linear operator Qa on given byThe iterative scheme is called vector subdivision scheme or vector cascade algorithm. The purpose of this paper is to provide a necessary and sufficient condition to guarantee the sequence to converge in L2-norm. As an application, we also characterize biorthogonal multiple refinable functions, which extends some main results in [B. Han, R.Q. Jia, Characterization of Riesz bases of wavelets generated from multiresolution analysis, Appl. Comput. Harmon. Anal., to appear] and [R.Q. Jia, Convergence of vector subdivision schemes and construction of biorthogonal multiple wavelets, Advances in Wavelet (Hong Kong, 1997), Springer, Singapore, 1998, pp. 199–227] to the general setting. 相似文献
6.
We relate asymptotics of Jacobi parameters to asymptotics of the spectral weights near the edges. Typical of our results is that for an≡1, bn=−Cn−β (), one has on (−2,2), and near x=2, where 相似文献
7.
Let k be an algebraically closed field of characteristic 2. We prove that the restricted nilpotent commuting variety , that is the set of pairs of (n×n)-matrices (A,B) such that A2=B2=[A,B]=0, is equidimensional. can be identified with the ‘variety of n-dimensional modules’ for , or equivalently, for k[X,Y]/(X2,Y2). On the other hand, we provide an example showing that the restricted nilpotent commuting variety is not equidimensional for fields of characteristic >2. We also prove that if e2=0 then the set of elements of the centralizer of e whose square is zero is equidimensional. Finally, we express each irreducible component of as a direct sum of indecomposable components of varieties of -modules. 相似文献
8.
The problem of finding the correct asymptotic rate of approximation by polynomial loops in dependence of the smoothness of the elements of a loop group seems not well-understood in general. For matrix Lie groups such as , it can be viewed as a problem of nonlinearly constrained trigonometric approximation. Motivated by applications to optical FIR filter design and control, we present some initial results for the case of -loops, N≥2. In particular, using representations via the exponential map and first order splitting methods, we prove that the best approximation of an -loop belonging to a Hölder–Zygmund class , α>1/2, by a polynomial -loop of degree ≤n is of the order O(n−α/(1+α)) as n→∞. Although this approximation rate is not considered final, to our knowledge it is the first general, nontrivial result of this type. 相似文献
9.
The zero sets of (D+a)ng(t) with in the (t,a)-plane are investigated for and .The results are used to determine entire interpolations to functions , which give representations for the best approximation and best one-sided approximation from the class of functions of exponential type η>0 to . 相似文献
10.
For any integers p,n≥2 necessary and sufficient conditions are given for scaling filters with pn many terms to generate a p-multiresolution analysis in . A method for constructing orthogonal compactly supported p-wavelets on is described. Also, an adaptive p-wavelet approximation in is considered. 相似文献
11.
Let , with
-1=x0n<x1n<<xnn<xn+1,n=1