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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Dernières modifications / Last modifications :  11 Janvier 2008