共查询到20条相似文献,搜索用时 15 毫秒
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Regularity results and critical group estimates are studied for critical (p, r)-systems. Multiplicity results of solutions for a critical potential quasilinear system are also proved using Morse theory. 相似文献
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Daniel S. Farley 《Transactions of the American Mathematical Society》2005,357(9):3567-3584
Picture groups are a class of groups introduced by Guba and Sapir. Known examples include Thompson's groups , , and .
In this paper, a large class of picture groups is proved to be of type . A Morse-theoretic argument shows that, for a given picture group, the rational homology vanishes in almost all dimensions.
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Houshang Behravesh Mohammad Hossein Jafari 《数学物理学报(B辑英文版)》2007,27(2):297-300
The quantities c(G), q(G) and p(G) for finite groups were defined by H. Behravesh. In this article, these quantities for the alternating group An and the symmetric group Sn are calculated. It is shown that c(G) = q(G)=p(G) = n, when G = An or Sn. 相似文献
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Hideaki Morita 《Advances in Mathematics》2007,212(1):277-292
We consider the Green polynomials at roots of unity. We obtain a recursive formula for the Green polynomials at roots of unity whose orders do not exceed some positive integer. The formula is described in a combinatorial manner. The coefficients of the recursive formula are realized by the cardinality of a set of permutations. The formula gives an interpretation of a combinatorial property on a family of graded modules for the symmetric group in terms of representation theory. 相似文献
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Alex Eskin 《Journal of the American Mathematical Society》1998,11(2):321-361
We compute the quasi-isometry group of an irreducible nonuniform lattice in a semisimple Lie group with finite center and no rank one factors, and show that any two such lattices are quasi-isometric if and only if they are commensurable up to conjugation.
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Morse Lemma是奇点理论中一个极为重要的结论。[1]的作者称其文中的定理1和定理2是Morse Lemma的推广。为此我们愿就[1]中的几个问题与[1]的作者商榷。 相似文献
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Pingan Zeng Jiaquan Liu Yuxia Guo 《Journal of Mathematical Analysis and Applications》2004,300(1):102-128
In this paper, by using the Morse index theory for strongly indefinite functionals developed in [Nonlinear Anal. TMA, in press], we compute precisely the critical groups at the origin and at infinity, respectively. The abstract theorems are used to study the existence (multiplicity) of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero. 相似文献
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Alexander S. Kleshchev Pham Huu Tiep 《Transactions of the American Mathematical Society》2004,356(5):1971-1999
Let be an algebraically closed field of characteristic and be an almost simple group or a central extension of an almost simple group. An important problem in representation theory is to classify the subgroups of and -modules such that the restriction is irreducible. For example, this problem is a natural part of the program of describing maximal subgroups in finite classical groups. In this paper we investigate the case of the problem where is the Schur's double cover or .
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Ruggero Freddi 《分析论及其应用》2022,38(1):26-78
In this paper we consider the Dirichlet problemwhere $\rho$ is a small parameter and $\Omega$ is a $C^2$ bounded domain in $\mathbb{R}^2$. In [1], the author proves the existence of a $m$-point blow-up solution $u_\rho$ jointly with its asymptotic behaviour. We compute the Morse index of $u_\rho$ in terms of the Morse index of the associated Hamilton function of this problem. In addition, we give an asymptotic estimate for the first $4m$ eigenvalues and eigenfunctions. 相似文献
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Robert Beals Charles R. Leedham-Green Alice C. Niemeyer Cheryl E. Praeger Á kos Seress 《Transactions of the American Mathematical Society》2003,355(5):2097-2113
We present a Las Vegas algorithm which, for a given black-box group known to be isomorphic to a symmetric or alternating group, produces an explicit isomorphism with the standard permutation representation of the group. This algorithm has applications in computations with matrix groups and permutation groups.
In this paper, we handle the case when the degree of the standard permutation representation is part of the input. In a sequel, we shall treat the case when the value of is not known in advance.
As an important ingredient in the theoretical basis for the algorithm, we prove the following result about the orders of elements of : the conditional probability that a random element is an -cycle, given that , is at least .
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Ilya Gorshkov 《代数通讯》2019,47(9):3905-3914
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Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group
representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces
of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo
invariant
Members of VBAC (Vector Bundles on Algebraic Curves). Second and Third authors partially supported by Ministerio de Educación
y Ciencia and Conselho de Reitores das Universidades Portuguesas through Acción Integrada Hispano-Lusa HP2002-0017 (Spain)/E–30/03
(Portugal). First and Second authors partially supported by Ministerio de Educación y Ciencia (Spain) through Project MTM2004-07090-C03-01.
Third author partially supported by the Centro de Matemática da Universidade do Porto and the project POCTI/MAT/58549/2004,
financed by FCT (Portugal) through the programmes POCTI and POSI of the QCA III (2000–2006) with European Community (FEDER)
and national funds. The second author visited the IHES with the partial support of the European Commission through its 6th
Framework Programme “Structuring the European Research Area” and the Contract No. RITA-CT-2004-505493 for the provision of
Transnational Access implemented as Specific Support Action 相似文献
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James P. Cossey 《代数通讯》2018,46(8):3356-3364
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Ravi P. Agarwal T. Gnana Bhaskar Kanishka Perera 《Journal of Mathematical Analysis and Applications》2014
We use Morse theory to study impulsive problems. First we consider asymptotically piecewise linear problems with superlinear impulses, and prove a new existence result for this class of problems using the saddle point theorem. Next we compute the critical groups at zero when the impulses are asymptotically linear near zero, in particular, we identify an important resonance set for this problem. As an application, we finally obtain a nontrivial solution for asymptotically piecewise linear problems with impulses that are asymptotically linear at zero and superlinear at infinity. Our results here are based on the simple observation that the underlying Sobolev space naturally splits into a certain finite dimensional subspace where all the impulses take place and its orthogonal complement that is free of impulsive effects. 相似文献
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Laércio J. dosSantos 《Indagationes Mathematicae》2007,18(1):135-146
Let G be a Lie group and L C G a Lie subgroup. We give necessary and sufficient conditions for a family of cosets of L to generate a subsemigroup with nonempty interior in G. We apply these conditions to symmetric pairs (G, L) where L is a subgroup of G such that Go C L C Gi and r is an involutive automorphism of G. As a consequence we prove that for several r the fixed point group GI is a maximal semigroup. 相似文献