SEMINAIRE
Mulhousien de MATHEMATIQUES
résumé/abstract
Karin
Baur (ETH Zürich)
$\Delta$-filtered modules for a
quasi-hereditary algebra
and adjoint orbits in a nilpotent
radical.
Consider a
parabolic subgroup of a reductive group $G$ (defined over an algebraically
closed field $K$). By a theorem of Richardson
(1974), it is well-known that the adjoint action of $P$ on its nilpotent
radical has an open dense orbit. In general, there is an infinite family of
orbits, so the description of the $P$-orbits is a ``wild'' problem. In type $A$
there exists a translation of this problem into a question of
representation-type of a category of representations of a path algebra due to
Hille and Röhrle (1999), namely the Auslander algebra of the truncated
polynomials $k[X]/X^r$. In this talk I will present our approach to generalize
this theory to type $D$. This is joint
work with Karin Erdmann (Oxford) and Alison
Parker (Leeds) .
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Séminaire Mulhousien de Mathématiques
Dernières modifications /
Last modifications : 11 Janvier 2008