L. Carbone

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20232026

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math.RT2026

Prosummability in Kac--Moody groups

Abid Ali, Lisa Carbone, Elizabeth Jurisich +1

Let $g$ be a symmetrizable Kac--Moody algebra. We describe {standard graded} $g$ -modules $V$ , which we use to construct a completion $V$ and pro-uni…

math.RT2024

Chevalley groups over $Z$ : A representation-theoretic approach

Abid Ali, Lisa Carbone, Scott H. Murray

Let $G (Q)$ be a simply connected Chevalley group over $Q$ corresponding to a simple Lie algebra $g$ over $C$ . Let $V$ be a finite dimensional f…

math.RT2024

Growth of root multiplicities along imaginary root strings in Kac--Moody algebras

Lisa Carbone, Terence Coelho, Scott H. Murray +2

Let $g$ be a symmetrizable Kac--Moody algebra. Given a root $α$ and a real root $β$ of $g$ , it is known that the $β$ -string through $α$ , denoted $R_{α} (β)$ , is…

math.RT2023

A Lie group analog for the Monster Lie algebra

Lisa Carbone, Elizabeth Jurisich, Scott H. Murray

The Monster Lie algebra $m$ , which admits an action of the Monster finite simple group $M$ , was introduced by Borcherds as part of his work on the Conway--Norton Mo…

Prosummability in Kac--Moody groups

Chevalley groups over Z: A representation-theoretic approach

Growth of root multiplicities along imaginary root strings in Kac--Moody algebras

A Lie group analog for the Monster Lie algebra

Chevalley groups over $Z$ : A representation-theoretic approach