667 research outputs found
From Jantzen to Andersen Filtration via Tilting Equivalence
The space of homomorphisms from a projective object to a Verma module in
category O inherits an induced filtration from the Jantzen filtration on the
Verma module. On the other hand there is the Andersen filtration on the space
of homomorphisms from a Verma module to a tilting module as described in
[Soe07]. The tilting equivalence from [Soe98] induces an isomorphism of these
kinds of Hom-spaces. We will show that this equivalence even identifies both
filtrations.Comment: 15 pages, minor typos correcte
Tilting modules in category O and sheaves on moment graphs
We describe tilting modules of the deformed category O over a semisimple Lie
algebra as certain sheaves on a moment graph associated to the corresponding
block of category O. We prove that they map to Braden-MacPherson sheaves
constructed along the reversed Bruhat order under Fiebig's localization
functor. By this means, we get character formulas for tilting modules and
explain how Soergel's result about the Andersen filtration gives a Koszul dual
proof of the semisimplicity of subquotients of the Jantzen filtration.Comment: 18 pages; minor typos and changes in chapter 5.
Equivariant Differential Cohomology
The construction of characteristic classes via the curvature form of a
connection is one motivation for the refinement of integral cohomology
by de Rham cocycles -- known as differential cohomology. We will discuss
the analog in the case of a group action on the manifold: We will show
the compatibility of the equivariant characteristic class in integral
Borel cohomology with the equivariant characteristic form in the Cartan
model. Motivated by this understanding of characteristic forms, we
define equivariant differential cohomology as a refinement of
equivariant integral cohomology by Cartan cocycles
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