共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Bernard Leclerc 《Algebras and Representation Theory》2000,3(3):277-287
We obtain some simple relations between decomposition numbers of quantized Schur algebras at an nth root of unity (over a field of characteristic 0). These relations imply that every decomposition number for such an algebra occurs as a decomposition number for some Hecke algebra of type A. We prove similar relations between coefficients of the canonical basis of the q-deformed Fock space representation of
. It follows that these coefficients can all be expressed in terms of those of the global crystal basis of the irreducible subrepresentation generated by the vacuum vector. As a consequence, using the works of Ariki and Varagnolo and Vasserot, it is possible to give a new proof of Lusztig"s character formula for the simple U
v
(sl
r
)-modules at roots of unity, which does not involve representations of
of negative level. 相似文献
3.
Guo Wei YU 《数学学报(英文版)》2022,(1):179-204
For a monotone twist map, under certain non-degenerate condition, we showed the existence of infinitely many homoclinic and heteroclinic orbits between two periodic neighboring minimal orbits with the same rotation number, which indicates chaotic dynamics. Our results also apply to geodesics of smooth Riemannian metrics on the two-dimension torus. 相似文献
4.
扭转映射的Aubry-Mather理论及其应用 总被引:1,自引:0,他引:1
本文介绍Aubry-Mather理论近年来的发展情况,文章讨论了该理论与KAM理论、保面积映射不动点理论的联系,并简单地介绍了它的一些推广。作为该理论的应用,对平面Hamil-ton系统Mather集的存在性给出了一些结果. 相似文献
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6.
This paper shows that a well-known algorithm proposed to compute the canonical polygonal schema of a surface can be transferred onto a 2-dimensional generalized map. We show that transformation rules on polygonal schemata can be achieved in O(1) with generalized maps, which can help optimizing existing algorithms. 相似文献
7.
Normal Bases and Their Dual-Bases over Finite Fields 总被引:2,自引:0,他引:2
Qun Ying LIAO Qi SUN 《数学学报(英文版)》2006,22(3):845-848
In this paper, we prove the following results: 1) A normal basis N over a finite field is equivalent to its dual basis if and only if the multiplication table of N is symmetric; 2) The normal basis N is self-dual if and only if its multiplication table is symmetric and Tr(α^2) = 1, where α generates N; 3) An optimal normal basis N is self-dual if and only if N is a type-Ⅰ optimal normal basis with q = n = 2 or N is a type-Ⅱ optimal normal basis. 相似文献
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Dual Bases for a New Family of Generalized Ball Bases 总被引:6,自引:0,他引:6
Hong-yiWu 《计算数学(英文版)》2004,22(1):79-88
This paper presents the dual bases for a new family of generalized Ball curves with a position parameter K, which includes the Bezier curve, generalized Said-Ball curve and some intermediate curves. Using the dual bases, the relative Marsden identity, conversion formulas of bases and control points of various curves are obtained. 相似文献
10.
Leandro Arosio 《Journal of Geometric Analysis》2017,27(2):1178-1210
We prove the existence and the essential uniqueness of canonical models for the forward (resp., backward) iteration of a holomorphic self-map f of a cocompact Kobayashi hyperbolic complex manifold, such as the ball \(\mathbb {B}^q\) or the polydisc \(\Delta ^q\). This is done by performing a time-dependent conjugacy of the autonomous dynamical system defined by f, obtaining in this way a non-autonomous dynamical system admitting a relatively compact forward (resp., backward) orbit, and then proving the existence of a natural complex structure on a suitable quotient of the direct limit (resp., subset of the inverse limit). As a corollary we prove the existence of a holomorphic solution with values in the upper half-plane of the Valiron equation for a hyperbolic holomorphic self-map of the unit ball. 相似文献
11.
We state new results concerning the zero sets of polynomials belonging to the dual canonical basis of mathbbC[x1, 1, . . . , xn, n]{mathbb{C}[x_1, 1, . . . , x_n, n]} . As an application, we show that this basis is related by a unitriangular transition matrix to the simpler bitableau basis popularized by Désarménien-Kung-Rota. It follows that spaces spanned by certain subsets of the dual canonical basis can be characterized in terms of products of matrix minors, or in terms of their common zero sets. 相似文献
12.
In this paper we show that there exist wavelet frames that have nice dual wavelet frames, but for which the canonical dual frame does not consist of wavelets, i.e., cannot be generated by the translates and dilates of a single function. 相似文献
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14.
Crystal Bases for Quantum Generalized Kac-Moody Algebras 总被引:2,自引:0,他引:2
Jeong Kyeonghoon; Kang Seok-Jin; Kashiwara Masaki 《Proceedings London Mathematical Society》2005,90(2):395-438
In this paper, we develop the crystal basis theory for quantumgeneralized KacMoody algebras. For a quantum generalizedKacMoody algebra Uq(g), we first introduce the categoryOint of Uq(g)-modules and prove its semisimplicity. Next, wedefine the notion of crystal bases for Uq(g)-modules in thecategory Oint and for the subalgebra . We then prove the tensor product rule and the existence theoremfor crystal bases. Finally, we construct the global bases forUq(g)-modules in the category Oint and for the subalgebra . 2000 Mathematics Subject Classification17B37, 17B67. 相似文献
15.
Emmanuel Schenck 《Annales Henri Poincare》2009,10(4):711-747
We study a toy model for “partially open” wave-mechanical system, like for instance a dielectric micro-cavity, in the semiclassical
limit where ray dynamics is applicable. Our model is a quantized map on the 2-dimensional torus, with an additional damping
at each time step, resulting in a subunitary propagator, or “damped quantum map”. We obtain analogues of Weyl’s laws for such
maps in the semiclassical limit, and draw some more precise estimates when the classical dynamics is chaotic.
Submitted: October 16, 2008. Accepted: April 3, 2009. 相似文献
16.
This paper generalizes the mixed extension principle in L
2(ℝ
d
) of (Ron and Shen in J. Fourier Anal. Appl. 3:617–637, 1997) to a pair of dual Sobolev spaces H
s
(ℝ
d
) and H
−s
(ℝ
d
). In terms of masks for φ,ψ
1,…,ψ
L
∈H
s
(ℝ
d
) and
, simple sufficient conditions are given to ensure that (X
s
(φ;ψ
1,…,ψ
L
),
forms a pair of dual wavelet frames in (H
s
(ℝ
d
),H
−s
(ℝ
d
)), where
For s>0, the key of this general mixed extension principle is the regularity of φ, ψ
1,…,ψ
L
, and the vanishing moments of
, while allowing
,
to be tempered distributions not in L
2(ℝ
d
) and ψ
1,…,ψ
L
to have no vanishing moments. So, the systems X
s
(φ;ψ
1,…,ψ
L
) and
may not be able to be normalized into a frame of L
2(ℝ
d
). As an example, we show that {2
j(1/2−s)
B
m
(2
j
⋅−k):j∈ℕ0,k∈ℤ} is a wavelet frame in H
s
(ℝ) for any 0<s<m−1/2, where B
m
is the B-spline of order m. This simple construction is also applied to multivariate box splines to obtain wavelet frames with short supports, noting
that it is hard to construct nonseparable multivariate wavelet frames with small supports. Applying this general mixed extension
principle, we obtain and characterize dual Riesz bases
in Sobolev spaces (H
s
(ℝ
d
),H
−s
(ℝ
d
)). For example, all interpolatory wavelet systems in (Donoho, Interpolating wavelet transform. Preprint, 1997) generated by an interpolatory refinable function φ∈H
s
(ℝ) with s>1/2 are Riesz bases of the Sobolev space H
s
(ℝ). This general mixed extension principle also naturally leads to a characterization of the Sobolev norm of a function in
terms of weighted norm of its wavelet coefficient sequence (decomposition sequence) without requiring that dual wavelet frames
should be in L
2(ℝ
d
), which is quite different from other approaches in the literature.
相似文献
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在文献[3]和[6]中,Hopf箭图的路代数上的Hopf代数结构和覆盖箭图的路余代数上的Hopf代数结构分别被给出.该文通过一个箭图是Hopf箭图当且仅当它是箭图覆盖这一结论,来讨论同一箭图上给出的这两种Hopf代数结构之间的对偶关系(见定理3和定理4).作为应用,作者先得到关于定向圈的路代数的商上的Hopf代数结构的一些性质,然后证明了Sweedler的4维-Hopf代数小仅是拟三角的而且是余拟三角的.最后,作者刻画了Schurian覆盖箭图的路代数上的Hopf代数的分次自同构群. 相似文献
19.
Lior Rosenzweig 《Annales Henri Poincare》2006,7(3):447-469
When a map is classically uniquely ergodic, it is expected that its quantization will posses quantum unique ergodicity. In
this paper we give examples of Quantum Unique Ergodicity for the perturbed Kronecker map, and an upper bound for the rate
of convergence.
submitted 3/02/05, accepted 20/10/05 相似文献
20.
For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra˙U and its canonical basis˙B given by Lusztig in 1992. In this paper, in the case that g is a symmetric Kac-Moody Lie algebra of finite or affine type, the authors define a set M which depends only on the root category R and prove that there is a bijection between M and ˙B, where R is the T~2-orbit category of the bounded derived category of the corresponding Dynkin or tame quiver. The method in this paper is based on a result of Lin, Xiao and Zhang in 2011, which gives a PBW-type basis of U~+. 相似文献