14 citations · 27 across the 5 of their papers we have counts for
5 papers
The Euclidean geometry of cardinal welfare functions
Tim Ridenour, Prasad Senesi
We exploit the standard inner product of Euclidean space to provide a new direction from which one can understand and analyze certain voting methods. Using this perspective along w…
ad-Nilpotent positively-graded Borel module subalgebras
Tim Ridenour, Adam Sandler
In this paper, we study certain ad-nilpotent subalgebras contained in the non-zero graded portion of a simple Z_n-graded Lie algebra. These subalgebras respect the grading on the L…
Faces of polytopes and Koszul algebras
Vyjayanthi Chari, Apoorva Khare, Tim Ridenour
Let $\g$ be a reductive Lie algebra and a $\g$-semisimple module. In this article, we study the category $\G$ of graded finite-dimensional representations of $\g \ltimes V$. We…
Faces of weight polytopes and a generalization of a theorem of Vinberg
Apoorva Khare, Tim Ridenour
The paper is motivated by the study of graded representations of Takiff algebras, cominuscule parabolics, and their generalizations. We study certain special subsets of the set of…
Ideals in Parabolic Subalgebras of Simple Lie Algebras
Vyjayanthi Chari, R. J. Dolbin, T. Ridenour
We study ad-nilpotent ideals of a parabolic subalgebra of a simple Lie algebra. Any such ideal determines an antichain in a set of positive roots of the simple Lie algebra. We give…