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Moduli spaces of local systems and higher Teichmüller theory

Vladimir Fock, Alexander Goncharov (2006)

Publications Mathématiques de l'IHÉS

Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic; the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When S have holes, we defined two moduli spaces closely...

Parity sheaves, moment graphs and the p -smooth locus of Schubert varieties

Peter Fiebig, Geordie Williamson (2014)

Annales de l’institut Fourier

We show that the Braden-MacPherson algorithm computes the stalks of parity sheaves. As a consequence we deduce that the Braden-MacPherson algorithm may be used to calculate the characters of tilting modules for algebraic groups and show that the p -smooth locus of a (Kac-Moody) Schubert variety coincides with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.

Singular localization of 𝔤 -modules and applications to representation theory

Erik Backelin, Kobi Kremnitzer (2015)

Journal of the European Mathematical Society

We prove a singular version of Beilinson–Bernstein localization for a complex semi-simple Lie algebra following ideas from the positive characteristic case settled by [BMR06]. We apply this theory to translation functors, singular blocks in the Bernstein–Gelfand–Gelfand category O and Whittaker modules.

Smooth components of Springer fibers

William Graham, R. Zierau (2011)

Annales de l’institut Fourier

This article studies components of Springer fibers for 𝔤𝔩 ( n ) that are associated to closed orbits of G L ( p ) × G L ( q ) on the flag variety of G L ( n ) , n = p + q . These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the action of a maximal torus of G L ( n ) . We prove that if ℒ is a line bundle on the flag variety associated to a dominant weight, then the higher...

Sous-groupes H -loxodromiques

Antonin Guilloux (2011)

Bulletin de la Société Mathématique de France

On considère une extension finie k de ℚ p , avec p un nombre premier, H un sous-groupe d’indice fini de k * et le groupe SL ( n , k ) . Nous montrons que SL ( n , k ) admet un sous-groupe ℚ p -Zariski-dense dont toutes les matrices ont leur spectre inclus dans H si et seulement si soit - 1 est dans le sous-groupe H , soit n n’est pas congru à 2 modulo 4.

Sur la cohomologie de la compactification des variétés de Deligne-Lusztig

Haoran Wang (2014)

Annales de l’institut Fourier

Nous étudions la cohomologie de la compactification des variétés de Deligne-Lusztig associées aux éléments de Coxeter. Nous présentons une conjecture des relations entre la cohomologie de la variété et la cohomologie de ses compactifications partielles. Nous prouvons la conjecture dans le cas du groupe linéaire général.

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