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Indefinite Kac-Moody
algebras of special linear type
Georgia Benkart, Seok-Jin Kang and Kailash C. Misra |
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Vol. 170 (1995), No. 2, 379–404
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Abstract |
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From the special linear Lie algebra An = sℓ(n + 1, ℂ) we construct certain indefinite Kac-Moody Lie algebras IAn(a,b) and then use the representation theory of An to determine explicit closed form root multiplicity formulas for the roots α of IAn(a,b) whose degree satisfies |deg(α)|≤ 2a + 1. These expressions involve the well-known Littlewood-Richardson coefficients and Kostka numbers. Using the Euler-Poincaré Principle and Kostant’s formula, we derive two expressions, one of which is recursive and the other closed form, for the multiplicity of an arbitrary root α of IAn(a,b) as a polynomial in Kostka numbers. |
Mathematical Subject Classification 2000
Primary: 17B67
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Milestones
Received: 25 February 1993
Published: 1 October 1995
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Authors |
| Georgia Benkart | |
| Department of Mathematics University of Wisconsin - Madison 480 Lincoln Drive Madison WI 53706 United States |
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| Seok-Jin Kang | |
| Kailash C. Misra | |
| Department of Mathematics North Carolina State University 2311 Stinson Drive Campus Box 8205 Raleigh NC 27695-8205 United States |
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| http://www4.ncsu.edu/~misra/ | |
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