1) La descarga del recurso depende de la página de origen
2) Para poder descargar el recurso, es necesario ser usuario registrado en Universia

Opción 1: Descargar recurso

Detalles del recurso


Suppose that $G$ is a complex, reductive algebraic group. A real form of $G$ is an antiholomorphic involutive automorphism $\sigma$ , so $G(\mathbb{R})=G(\mathbb{C})^{\sigma}$ is a real Lie group. Write $H^{1}(\sigma,G)$ for the Galois cohomology (pointed) set $H^{1}(\operatorname{Gal}(\mathbb{C}/\mathbb{R}),G)$ . A Cartan involution for $\sigma$ is an involutive holomorphic automorphism $\theta$ of $G$ , commuting with $\sigma$ , so that $\theta\sigma$ is a compact real form of $G$ . Let $H^{1}(\theta,G)$ be the set $H^{1}(\mathbb{Z}_{2},G)$ , where the action of the nontrivial element of $\mathbb{Z}_{2}$ is by $\theta$ . By analogy with the Galois group, we refer to $H^{1}(\theta,G)$ as the Cartan cohomology of $G$ with respect to $\theta$ . Cartan’s classification of real forms of a connected group, in terms of their maximal compact subgroups, amounts to an isomorphism $H^{1}(\sigma,G_{\mathrm{ad}})\simeq H^{1}(\theta,G_{\mathrm{ad}})$ , where $G_{\mathrm{ad}}$ is the adjoint group. Our main result is a generalization of this: there is a canonical isomorphism $H^{1}(\sigma,G)\simeq H^{1}(\theta,G)$ . ¶ We apply this result to give simple proofs of some well-known structural results: the Kostant–Sekiguchi correspondence of nilpotent orbits; Matsuki duality of orbits on the flag variety; conjugacy classes of Cartan subgroups; and structure of the Weyl group. We also use it to compute $H^{1}(\sigma,G)$ for all simple, simply connected groups and to give a cohomological interpretation of strong real forms. For the applications it is important that we do not assume that $G$ is connected.

Pertenece a

Project Euclid (Hosted at Cornell University Library)  


Adams, Jeffrey -  Taïbi, Olivier - 

Id.: 71215093

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveGalois cohomology - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 Duke University Press

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0012-7094
[References] 1547-7398

Fecha de contribución: 14-abr-2018


* Duke Math. J. 167, no. 6 (2018), 1057-1097
* doi:10.1215/00127094-2017-0052

Otros recursos del mismo autor(es)

  1. Arthur's multiplicity formula for $GSp_4$ and restriction to $Sp_4$ We prove the classification of discrete automorphic representations of $GSp_4$ explained in [Art04],...
  2. Contragredient representations and characterizing the local Langlands correspondence We consider the question: what is the contragredient in terms of L-homomorphisms? We conjecture that...
  3. Eigenvarieties for classical groups and complex conjugations in Galois representations The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor des...
  4. Dimensions of spaces of level one automorphic forms for split classical groups using the trace formula 89 pages, 28 tables, comments welcome. Much more data available at http://www.math.ens.fr/~taibi/dim...
  5. $rec.titulo

Otros recursos de la mismacolección

  1. The $p$ -curvature conjecture and monodromy around simple closed loops The Grothendieck–Katz $p$ -curvature conjecture is an analogue of the Hasse principle for differenti...
  2. Analytic torsion and R-torsion of Witt representations on manifolds with cusps We establish a Cheeger–Müller theorem for unimodular representations satisfying a Witt condition on ...
  3. A minimization problem with free boundary related to a cooperative system We study the minimum problem for the functional \begin{equation*}\int_{\Omega}(\vert\nabla\mathbf{u}...
  4. Independence of $\ell$ for the supports in the decomposition theorem In this article, we prove a result on the independence of $\ell$ for the supports of irreducible per...
  5. Universal dynamics for the defocusing logarithmic Schrödinger equation We consider the Schrödinger equation with a logarithmic nonlinearity in a dispersive regime. We show...

Aviso de cookies: Usamos cookies propias y de terceros para mejorar nuestros servicios, para análisis estadístico y para mostrarle publicidad. Si continua navegando consideramos que acepta su uso en los términos establecidos en la Política de cookies.