Modelling Richardson Orbits for Son via ∆-filtered Modules
نویسنده
چکیده
We study the ∆-filtered modules for the Auslander algebra of k[T ]/Tn ⋊C2 where C2 is the cyclic group of order two. The motivation for this is the bijection between parabolic orbits in the nilradical of a parabolic subgroup of SLn and certain ∆-filtered modules for the Auslander algebra of k[T ]/Tn as found by Hille and Röhrle and Brüstle et al., cf. [HR99] [BHRR99]. Under this bijection, the Richardson orbit (i.e. the dense orbit) corresponds to the ∆-filtered module without self-extensions. It has remained an open problem to describe such a correspondence for other classical groups. In this paper, we establish the Auslander algebra of k[T ]/Tn ⋊ C2 as the right candidate for the orthogonal groups. In particular, for any parabolic subgroup of an orthogonal group we construct a map from parabolic orbits to ∆-filtered modules and show that in the case of the Richardson orbit, the result has no self-extensions. One of the consequences of our work is that we are able to describe the extensions between special classes of ∆-filtered modules. In particular, we show that these extensions can grow arbitrarily large.
منابع مشابه
Vanishing of Ext-Functors and Faltings’ Annihilator Theorem for relative Cohen-Macaulay modules
et be a commutative Noetherian ring, and two ideals of and a finite -module. In this paper, we have studied the vanishing and relative Cohen-Macaulyness of the functor for relative Cohen-Macauly filtered modules with respect to the ideal (RCMF). We have shown that the for relative Cohen-Macaulay modules holds for any relative Cohen-Macauly module with respect to with ........
متن کاملExtension of Krull's intersection theorem for fuzzy module
In this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules. It shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $mu$-adic comp...
متن کاملON ORBITAL VARIETY CLOSURES IN sln II. DESCENDANTS OF A RICHARDSON ORBITAL VARIETY
For a semisimple Lie algebra g the orbit method attempts to assign representations of g to (coadjoint) orbits in g∗. Orbital varieties are particular Lagrangian subvarieties of such orbits leading to highest weight representations of g. In sln orbital varieties are described by Young tableaux. In this paper we consider so called Richardson orbital varieties in sln. A Richardson orbital variety ...
متن کاملPurity and Gorenstein Filtered Rings
In this paper, we discuss on the existence of filtrations of modules having good properties. In particular, we focus on filtered homomorphisms called strict, and show that there exists a filtration which makes a filtered homomorphism a strict filtered homomorphism. Moreover, by using this result, we study purity for filtered modules over a Gorenstein filtered ring.
متن کامل