Quiver-graded Richardson orbits. Issue 10 (3rd October 2019)

• Record Type: Journal Article
• Authors: Eiríksson, Ögmundur; Sauter, Julia
• Is Part Of: Communications in algebra. Volume 47:Issue 10(2019)
• Page Start: 4304
• Page End: 4335
• Publication Date: 2019-10-03
• Subjects: Quiver Grassmannian -- representation variety -- quasi-hereditary algebra -- recollement; Primary 14L30 -- Secondary 16G10 -- 14M15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1588974
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: In Lie theory, a dense orbit in the nilpotent radical of a parabolic group under the operation of the parabolic is called a Richardson orbit. We define a quiver-graded version of Richardson orbits generalizing the classical definition in the case of the general linear group. We define a quasi-hereditary algebra called the nilpotent quiver algebra whose isomorphism classes of Δ-filtered modules correspond to orbits in our generalized setting. We translate the existence of a Richardson orbit into the existence of a rigid Δ-filtered module of a given dimension vector. We study an idempotent recollement of this algebra whose associated intermediate extension functor can be used to produce Richardson orbits in some situations. This can be explicitly calculated in examples. We also give examples where no Richardson orbit exists.