共查询到20条相似文献,搜索用时 12 毫秒
1.
Matvei Libine 《Journal of Functional Analysis》2003,203(1):197-236
This article provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed by Schmid (in: Deformation Theory and Symplectic Geometry, Mathematical Physics Studies, Vol. 20, Kluwer Academic Publishers, Dordrecht, 1997, pp. 259-270).A corresponding problem in the compact group setting was solved by Berline et al. (Heat Kernels and Dirac Operators, Springer, Berlin, 1992) by an application of the theory of equivariant forms and particularly the fixed point integral localization formula. This article (besides its representation-theoretical significance) provides a whole family of examples where it is possible to localize integrals to fixed points with respect to an action of a noncompact group. Moreover, a localization argument given here is not specific to the particular setting considered in this article and can be extended to a more general situation.There is a broadly accessible article (Libine, A Localization Argument for Characters of Reductive Lie Groups: An Introduction and Examples, 2002, math.RT/0208024) which explains how the argument works in the case, where the key ideas are not obstructed by technical details and where it becomes clear how it extends to the general case. 相似文献
2.
Matvei Libine 《Journal of Functional Analysis》2004,215(1):50-66
Let be a Lie group acting on an oriented manifold M, and let ω be an equivariantly closed form on M. If both and M are compact, then the integral is given by the fixed point integral localization formula (Theorem 7.11 in Berline et al. Heat Kernels and Dirac Operators, Springer, Berlin, 1992). Unfortunately, this formula fails when the acting Lie group is not compact: there simply may not be enough fixed points present. A proposed remedy is to modify the action of in such a way that all fixed points are accounted for.Let be a real semisimple Lie group, possibly noncompact. One of the most important examples of equivariantly closed forms is the symplectic volume form dβ of a coadjoint orbit Ω. Even if Ω is not compact, the integral exists as a distribution on the Lie algebra . This distribution is called the Fourier transform of the coadjoint orbit.In this article, we will apply the localization results described in [L1,L2] to get a geometric derivation of Harish-Chandra's formula (9) for the Fourier transforms of regular semisimple coadjoint orbits. Then, we will make an explicit computation for the coadjoint orbits of elements of which are dual to regular semisimple elements lying in a maximally split Cartan subalgebra of . 相似文献
3.
We give an algebro-geometric derivation of the known intersection theory on the moduli space of stable rank 2 bundles of odd degree over a smooth curve of genus g. We lift the computation from the moduli space to a Quot scheme, where we obtain the intersections via equivariant localization with respect to a natural torus action. 相似文献
4.
We apply the “homotopy coniveau” machinery developed by the first-named author to the K-theory of coherent G-sheaves on a finite type G-scheme X over a field, where G is a finite group. This leads to a definition of G-equivariant higher Chow groups (different from the Chow groups of classifying spaces constructed by Totaro and generalized
to arbitrary X by Edidin–Graham) and an Atiyah–Hirzebruch spectral sequence from the G-equivariant higher Chow groups to the higher K-theory of coherent G-sheaves on X. This spectral sequence generalizes the spectral sequence from motivic cohomology to K-theory constructed by Bloch–Lichtenbaum and Friedlander–Suslin.
The first-named author gratefully acknowledges the support of the Humboldt Foundation through the Wolfgang Paul Program, and
support of the NSF via grants DMS-0140445 and DMS-0457195. 相似文献
5.
Detlev W. Hoffmann 《Transactions of the American Mathematical Society》1996,348(8):3267-3281
Let and be anisotropic quadratic forms over a field of characteristic not . Their function fields and are said to be equivalent (over ) if and are isotropic. We consider the case where and is divisible by an -fold Pfister form. We determine those forms for which becomes isotropic over if , and provide partial results for . These results imply that if and are equivalent and , then is similar to over . This together with already known results yields that if is of height and degree or , and if , then and are equivalent iff and are isomorphic over .
6.
Wai Kiu Chan Byeong Moon Kim Myung-Hwan Kim Byeong-Kweon Oh 《The Ramanujan Journal》2008,17(1):145-153
Let N and M be quadratic ?-lattices, and K be a sublattice of N. A representation σ:K→M is said to be extensible to N if there exists a representation ρ:N→M such that ρ | K =σ. We prove in this paper a local–global principle for extensibility of representation, which is a generalization of the main theorems on representations by positive definite ?-lattices by Hsia, Kitaoka and Kneser (J. Reine Angew. Math. 301:132–141, 1978) and Jöchner and Kitaoka (J. Number Theory 48:88–101, 1994). Applications to almost n-universal lattices and systems of quadratic equations with linear conditions are discussed. 相似文献
7.
We complete a classification of quadratic forms over a field of characteristic 2 of type (1,3) that become isotropic over the function field of a quadric. 相似文献
8.
Sergei M. Ageev Dusan Repovs 《Proceedings of the American Mathematical Society》2002,130(5):1539-1550
Ancel's method of fiberwise trivial relations is applied to the problem of characterization of absolute equivariant extensors. We obtain a generalization of Jaworowski's theorem on characterization of equivariant extensors lying in to the case when the space is infinite-dimensional, has infinitely many orbit types and the acting compact group is not necessarily a Lie group.
9.
Let X be a projective complex K 3 surface. Beauville and Voisin singled out a 0-cycle cX on X of degree 1 and Huybrechts proved that the second Chern class of a rigid simple vector-bundle on X is a multiple of cX if certain hypotheses hold. We believe that the following generalization of Huybrechts? result holds. Let M be a moduli space of stable pure sheaves on X with fixed cohomological Chern character: the set whose elements are second Chern classes of sheaves parametrized by the closure of M (in the corresponding moduli spaces of semistable sheaves) depends only on the dimension of M. We will prove that the above statement holds under some additional assumptions on the Chern character. 相似文献
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In this paper, we calculate the exact asymptotics with remainder of integrals of Laplace type in an arbitrary space, without imposing any constraints on the smoothness of the functions. As a special case, we derive the classical Laplace formula. Some examples are given. 相似文献
13.
We consider the equilibrium problem for a plate with a crack. The equilibrium of a plate is described by the biharmonic equation. Stress free boundary conditions are given on the crack faces. We introduce a perturbation of the domain in order to obtain an invariant Cherepanov–Rice-type integral which gives the energy release rate upon the quasistatic growth of a crack. We obtain a formula for the derivative of the energy functional with respect to the perturbation parameter which is useful in forecasting the development of a crack (for example, in study of local stability of a crack). The derivative of the energy functional is representable as an invariant integral along a sufficiently smooth closed contour. We construct some invariant integrals for the particular perturbations of a domain: translation of the whole cut and local translation along the cut. 相似文献
14.
Integral curves of characteristic vector fields of real hypersurfaces in nonflat complex space forms
In this paper, we study real hypersurfaces all of whose integral curves of characteristic vector fields are plane curves in
a nonflat complex space form.
相似文献
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16.
Lakhdar Meziani 《Proceedings of the American Mathematical Society》2002,130(7):2067-2077
Let be a compact space and let , be a (real, for simplicity) Banach space. We consider the space of all continuous -valued functions on , with the supremum norm .
which satisfy the following condition:
where is the conjugate space of . In the particular case where , this condition is obviously satisfied by every bounded linear operator
and the result reduces to the classical Riesz representation theorem.
We prove in this paper a Bochner integral representation theorem for bounded linear operators
which satisfy the following condition:
where is the conjugate space of . In the particular case where , this condition is obviously satisfied by every bounded linear operator
and the result reduces to the classical Riesz representation theorem.
If the dimension of is greater than , we show by a simple example that not every bounded linear admits an integral representation of the type above, proving that the situation is different from the one dimensional case.
Finally we compare our result to another representation theorem where the integration process is performed with respect to an operator valued measure.
17.
Najib Ouled Azaiez 《Journal of Number Theory》2008,128(7):1966-1988
We describe the additive structure of the graded ring of quasimodular forms over any discrete and cocompact group Γ⊂PSL(2,R). We show that this ring is never finitely generated. We calculate the exact number of new generators in each weight k. This number is constant for k sufficiently large and equals where I and are the ideals of modular forms and quasimodular forms, respectively, of positive weight. We show that is contained in some finitely generated ring of meromorphic quasimodular forms with i.e., the same order of growth as 相似文献
18.
We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures. 相似文献
19.
洪晓春 《数学的实践与认识》2010,40(3)
利用Picard-Fuchs方程法及Riccati方程法,研究了一类二次可逆系统在任意n次多项式扰动下Abel积分零点个数的上界问题,得到了当n≥4时,上界为10n+[n/2]-1. 相似文献
20.
We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures. 相似文献