The Δ-Filtered Modules Without Self-Extensions for the Auslander Algebra of k[ T ]/〈 T n 〉

摘要: It is well known that the Auslander algebra of any representation finite quasi-hereditary. We consider A n k[T]/〈 〉 (here, k a field, T variable and n natural number). determine all Δ-filtered -modules without self-extensions. They can be described purely combinatorially. Given module N, we show there (up to isomorphism) unique M self-extensions which has same dimension vector. In case where an infinite N degeneration this M. particular, see in case, set modules with fixed vector closure open orbit (thus irreducible). As observed by Hille Rohrle, problem describing as conjugacy classes elements unipotent radical parabolic subgroup P GL(m, k) under action P, thus recover Richardson's dense theorem instance.