8 citations · 16 across the 12 of their papers we have counts for
16 papers
Reduction rules for Demazure modules
Marc Besson, Sam Jeralds, Joshua Kiers
For a complex reductive group and a Borel subgroup, we provide a reduction rule for certain weight multiplicities in Demazure modules : given a weight $μ…
Geometric invariant theory and stretched Kostka quasi-polynomials
Marc Besson, Sam Jeralds, Joshua Kiers
For a semisimple, simply-connected complex algebraic group and two dominant integral weights , we consider the dimensions of weight spaces of weight in the i…
Affine Demazure Weight Polytopes and Twisted Bruhat Orders
Marc Besson, Sam Jeralds, Joshua Kiers
For an untwisted affine Kac-Moody Lie algebra with Cartan and Borel subalgebras , affine Demazure modules are…
Vertices in multiplicative eigenvalue problem for arbitrary groups
Prakash Belkale, Joshua Kiers
We determine, in an inductive framework, the vertices of the polytope controlling the conjugacy classes of elements which product to one in the maximal compact subgroup $K…
Disentangling the Seesaw in the Left-Right Model -- An Algorithm for the General Case
Joshua Kiers, Ken Kiers, Alejandro Szynkman +1
Senjanovic and Tello have analyzed how one could determine the neutrino Dirac mass matrix in the minimal left-right model, assuming that the mass matrices for the light and heavy n…
Weight polytopes and saturation of Demazure characters
Marc Besson, Sam Jeralds, Joshua Kiers
For a reductive group and a maximal torus and Borel subgroup, Demazure modules are certain -submodules, indexed by elements of the Weyl group, of the finite irr…
Extremal rays of the equivariant Littlewood-Richardson cone
Joshua Kiers
We give an inductive procedure for finding the extremal rays of the equivariant Littlewood-Richardson cone, which is closely related to the solution space to S. Friedland's majoriz…
The Kostka semigroup and its Hilbert basis
Shiliang Gao, Joshua Kiers, Gidon Orelowitz +1
The Kostka semigroup consists of pairs of partitions with at most r parts that have positive Kostka coefficient. For this semigroup, Hilbert basis membership is an NP-complete prob…
Weyl's problem: A computational approach
Isaac Bowser, Ken Kiers, Erica Mitchell +1
The distribution of eigenvalues of the wave equation in a bounded domain is known as Weyl's problem. We describe several computational projects related to the cumulative state numb…
Vertices of Intersection Polytopes and Rays of Generalized Kostka Cones
Marc Besson, Sam Jeralds, Joshua Kiers
Let be the rational cone generated by pairs where and are dominant integral weights and is a nontrivial weight space in the representation $V_…
Extremal rays of the embedded subgroup saturation cone
Joshua Kiers
We examine the extremal rays of the cone of dominant weights for groups for which there exists such that $$ \left(V(Nμ)\otimes V(N…
Multiplicity in root components via Geometric Satake
Marc Besson, Sam Jeralds, Joshua Kiers
In this note we explicitly construct top-dimensional components of the cyclic convolution varieties. These components correspond (via the geometric Satake equivalence) to irreducib…
A proof of the refined PRV conjecture via the cyclic convolution variety
Joshua Kiers
In this brief note we illustrate the utility of the geometric Satake correspondence by employing the cyclic convolution variety to give a simple proof of the Parthasarathy-Ranga Ra…
On the saturation conjecture for
Joshua Kiers
In this paper we examine the saturation conjecture on decompositions of tensor products of irreducible representations for complex semisimple algebraic groups of type (the even…
Extremal rays in the Hermitian eigenvalue problem for arbitrary types
Prakash Belkale, Joshua Kiers
The Hermitian eigenvalue problem asks for the possible eigenvalues of a sum of Hermitian matrices given the eigenvalues of the summands. This is a problem about the Lie algebra of…
Extending Hypothesis Testing with Persistence Homology to Three or More Groups
Christopher Cericola, Inga Johnson, Joshua Kiers +3
We extend the work of Robinson and Turner to use hypothesis testing with persistence homology to test for measurable differences in shape between point clouds from three or more gr…