Vol. 7, No. 4, 2014

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Investigating root multiplicities in the indefinite Kac–Moody algebra $E_{10}$

Vicky Klima, Timothy Shatley, Kyle Thomas and Andrew Wilson

Vol. 7 (2014), No. 4, 529–546
Abstract

Following a procedure outlined by Kang, we view the generalized eigenspaces, known as root spaces, of the infinite dimensional Kac–Moody algebra E10 as generalized eigenspaces for representations of the finite dimensional special linear algebra A9. Then, using the combinatorial representation theory of the special linear Lie algebras, we determine the dimensions of certain root spaces in E10.

Keywords
Kac–Moody, representation theory, combinatorial representation theory, root multiplicity
Mathematical Subject Classification 2010
Primary: 17B67
Milestones
Received: 17 January 2013
Accepted: 2 June 2013
Published: 31 May 2014

Communicated by Jim Haglund
Authors
Vicky Klima
Department of Mathematical Sciences
Appalachian State University
121 Bodenheimer Drive
Boone, NC 28607
United States
Timothy Shatley
Department of Mathematics
Louisiana State University
Baton Rouge, LA 70803-4918
United States
Kyle Thomas
Department of Mathematical Sciences
Appalachian State University
121 Bodenheimer Drive
Boone, NC 28607
United States
Andrew Wilson
Department of Mathematical Sciences
Appalachian State University
121 Bodenheimer Drive
Boone, NC 28607
United States