4 papers
math.RT2026
Prosummability in Kac--Moody groups
Abid Ali, Lisa Carbone, Elizabeth Jurisich +1
Let be a symmetrizable Kac--Moody algebra. We describe {standard graded} -modules , which we use to construct a completion and pro-uni…
math.RT2024
Chevalley groups over : A representation-theoretic approach
Abid Ali, Lisa Carbone, Scott H. Murray
Let be a simply connected Chevalley group over corresponding to a simple Lie algebra over . Let 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 be a symmetrizable Kac--Moody algebra. Given a root and a real root of , it is known that the -string through , denoted , is…
math.RT2023
A Lie group analog for the Monster Lie algebra
Lisa Carbone, Elizabeth Jurisich, Scott H. Murray
The Monster Lie algebra , which admits an action of the Monster finite simple group , was introduced by Borcherds as part of his work on the Conway--Norton Mo…