The \(\Delta\)-filtered modules without self-extensions for the Auslander algebra of \(k[T]/\langle T^n\rangle\)
In an earlier paper [Transform. Groups 4, No. 1, 35-52 (1999; Zbl 0924.20035)], two of the present authors showed that the problem of describing conjugacy classes under the action of a parabolic subgroup of a general linear group acting on its unipotent radical, is equivalent to the problem of describing the \(\Delta\)-filtered modules over the Auslander algebra of \(k[T]/\langle T^n\rangle\) for some \(n\). The present paper studies these \(\Delta\)-filtered modules, in particular those without self-extensions which are classified in a purely combinatorial way. In fact, an indecomposable such module is determined by its \(\Delta\)-dimension vector.
scientific article; zbMATH DE number 1385255