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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
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Abstract |
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Following a procedure outlined by Kang, we view the generalized eigenspaces, known as root spaces, of the infinite dimensional Kac–Moody algebra as generalized eigenspaces for representations of the finite dimensional special linear algebra . Then, using the combinatorial representation theory of the special linear Lie algebras, we determine the dimensions of certain root spaces in . |
Keywords
Kac–Moody, representation theory, combinatorial
representation theory, root multiplicity
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Mathematical Subject Classification 2010
Primary: 17B67
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Milestones
Received: 17 January 2013
Accepted: 2 June 2013
Published: 31 May 2014
Communicated by Jim Haglund
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Authors |
| Vicky Klima | |
| Department of Mathematical
Sciences Appalachian State University 121 Bodenheimer Drive Boone, NC 28607 United States |
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| Timothy Shatley | |
| Department of Mathematics Louisiana State University Baton Rouge, LA 70803-4918 United States |
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| Kyle Thomas | |
| Department of Mathematical
Sciences Appalachian State University 121 Bodenheimer Drive Boone, NC 28607 United States |
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| Andrew Wilson | |
| Department of Mathematical
Sciences Appalachian State University 121 Bodenheimer Drive Boone, NC 28607 United States |
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