1. Delta-filtered representations of double quivers and seaweed Lie algebras of affine type A
- Author
-
Brown, Robert, Su, Xiuping, and Traustason, Gunnar
- Subjects
quiver representations ,affine Lie algebras ,seaweed subalgebras - Abstract
By Richardson's Theorem, there exists a dense open adjoint orbit in the nilpotent radical of any parabolic subalgebra of a semisimple Lie algebra. Elements contained in this orbit are called Richardson elements. Jensen, Su and Yu generalised the study of Richardson elements to seaweed (biparabolic) subalgebras, using ∆-filtered modules of a quasi-hereditary algebra arising as a quotient of the path algebra of a double quiver. In this thesis, we extend the study of these quiver representations to affine type A, providing an explicit construction for a general ∆-filtered representation and a classification of the existence of open orbits in terms of the ∆-dimension vector. This allows us to give a combinatorial classification for the existence of Richardson elements in proper standard seaweed subalgebras of non-twisted affine Lie algebras of type A.
- Published
- 2022