Delta-filtered modules and nilpotent orbits of a parabolic subgroup in O_N.

Delta-filtered modules and nilpotent orbits of a parabolic subgroup in O_N.

Thu, 12/05/2011
14:30 		Alison Parker (Leeds) Representation Theory Seminar Add to calendar L3
Delta-filtered modules and nilpotent orbits of a parabolic subgroup in O_N.
In joint work with Karin Baur (ETH, Zurich) and Karin Erdmann (Oxford), we study certain Delta-filtered modules for the Auslander algebra of k[T]/T^n\rtimes C_2 where C_2 is the cyclic group of order two. The motivation of this lies in the problem of describing the $ P $-orbit structure for the action of a parabolic subgroup $ P $ of a linear algebraic group on its nilradical \mathfrak{n}. In general, there are infinitely P-orbits in \mathfrak{n} and it is a “wild” problem to describe them. However, in the case of a parabolic subgroup of SL_N, there exists a bijection between P-orbits in the nilradical and certain (Delta-filtered) modules for the Auslander algebra of k[T]/T^n, due to work of Hille and Rohrle and Brustle et al.. Under this bijection, the Richardson orbit (i.e. the dense orbit) corresponds to the Delta-filtered module without self-extensions. It has remained an open problem to describe such a correspondence for other classical groups.