Topic
Equivariant map
About: Equivariant map is a research topic. Over the lifetime, 9205 publications have been published within this topic receiving 137115 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the authors studied equivariant families of discrete Hamiltonians on amenable geometries and their integrated density of states (IDS) and proved that the eigenspace of a fixed energy is spanned by eigenfunctions with compact support.
Abstract: We study equivariant families of discrete Hamiltonians on amenable geometries and their integrated density of states (IDS). We prove that the eigenspace of a fixed energy is spanned by eigenfunctions with compact support. The size of a jump of the IDS is consequently given by the equivariant dimension of the subspace spanned by such eigenfunctions. From this we deduce uniform convergence (w.r.t. the spectral parameter) of the finite volume approximants of the IDS. Our framework includes quasiperiodic operators on Delone sets, periodic and random operators on quasi-transitive graphs, and operators on percolation graphs.
33 citations
TL;DR: In this paper, the geometry of Kuchle varieties with Picard number greater than 1 was described, and the structure of their derived categories was also described, as well as their structure of derived categories.
Abstract: We describe the geometry of Kuchle varieties (that is, Fano fourfolds of index 1 contained in Grassmannians as zero loci of sections of equivariant vector bundles) with Picard number greater than 1. We also describe the structure of their derived categories.
33 citations
TL;DR: In this paper, the authors extend the ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points, and prove the existence of integral canonical classes in the case that the moment map component is index increasing.
Abstract: The main purpose of this article is to extend some of the ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. Given a generic component of the moment map, we define a canonical class \alpha_p in the equivariant cohomology of the manifold M for each fixed point p of M. When they exist, canonical classes form a natural basis of the equivariant cohomology of M; in particular, when M is a flag variety, these classes are the equivariant Schubert classes. We show that the restriction of a canonical class \alpha_p to a fixed point q can be calculated by a rational function which depends only on the value of the moment map, and the restriction of other canonical classes to points of index exactly two higher. Therefore, the structure constants can be calculated by a similar rational function. Our restriction formula is manifestly positive in many cases, including when M is a flag manifold. Finally, we prove the existence of integral canonical classes in the case that M is a GKM manifold the moment map component is index increasing. In this case, our restriction formula specializes to an easily computable rational sum which depends only on the GKM graph.
33 citations
Posted Content•
TL;DR: In this paper, an equivalence between the derived category of equivariant coherent sheaves on the cotangent bundle to the flag variety of a simple algebraic group was constructed.
Abstract: In math.RT/0201073 we constructed an equivalence between the derived category of equivariant coherent sheaves on the cotangent bundle to the flag variety of a simple algebraic group and a (quotient of) the category of constructible sheaves on the affine flag variety of the Langlands dual group. Below we prove certain properties of this equivalence; provide a similar ``Langlands dual'' description for the category of equivariant coherent sheaves on the nilpotent cone; and deduce some conjectures by Lusztig and Ostrik.
33 citations
TL;DR: In this paper, the second part of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula is presented.
Abstract: This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result [KR1, Th. 4.4] of the first paper to prove a residue formula ”`a la Bott” for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of BismutGoette on the equivariant (Ray-Singer) analytic torsion play a key role in
33 citations