Sam Jeralds

activity

20212026

collaborators

4 papers

math.RT2026

Components of $V (m ρ) \otimes V (n ρ)$

Rekha Biswal, Sam Jeralds

Let $g$ be a symmetrizable Kac-Moody Lie algebra and let $ρ$ denote the sum of the fundamental weights. The irreducible highest weight representations $V (m ρ)$ occupy a d…

math.RT2022

Components of $V (ρ) \otimes V (ρ)$ and dominant weight polyhedra for affine Kac-Moody Lie algebras

Sam Jeralds, Shrawan Kumar

Kostant asked the following question: Let $g$ be a simple Lie algebra over the complex numbers. Let $λ$ be a dominant integral weight. Then, $V (λ)$ is a component of $V(…

math.RA2021

Toward a Jacobson--Morozov theorem for Kac--Moody Lie algebras

Sam Jeralds

For a finite-dimensional semisimple Lie algebra $g$ , the Jacobson--Morozov theorem gives a construction of subalgebras $sl_{2} \subset g$ correspondi…

math.RT2021

Root components for tensor product of affine Kac-Moody Lie algebra modules

Samuel Jeralds, Shrawan Kumar

Let g be an affine Kac-Moody Lie algebra and let $λ, μ$ be two dominant integral weights for g. We prove that under some mild restriction, for any positive root $β$ , $V(λ)\otimes V…

Components of V(mρ)⊗V(nρ)

Components of V(ρ)⊗V(ρ) and dominant weight polyhedra for affine Kac-Moody Lie algebras

Toward a Jacobson--Morozov theorem for Kac--Moody Lie algebras

Root components for tensor product of affine Kac-Moody Lie algebra modules

Components of $V (m ρ) \otimes V (n ρ)$

Components of $V (ρ) \otimes V (ρ)$ and dominant weight polyhedra for affine Kac-Moody Lie algebras