Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2019; 34(4): 1079-1098

Online first article August 27, 2019      Printed October 31, 2019

https://doi.org/10.4134/CKMS.c180373

Copyright © The Korean Mathematical Society.

Some branching formulas for Kac--Moody Lie algebras

Kyu-Hwan Lee, Jerzy Weyman

University of Connecticut; University of Connecticut

Abstract

In this paper we give some branching rules for the fundamental representations of Kac--Moody Lie algebras associated to $T$-shaped graphs. These formulas are useful to describe generators of the generic rings for free resolutions of length three described in \cite{JWm18}. We also make some conjectures about the generic rings.

Keywords: Kac--Moody algebras, branching formulas

MSC numbers: 13C99, 13H10

Supported by: K.-H. Lee was partially supported by a grant from the Simons Foundation (#318706).
J. Weyman was partly supported by NSF DMS grant 1802067.

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