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Imaginary Roots of a Kac-Moody Lie Algebra Whose Reflections Preserve Root Multiplicities

โœ Scribed by C. Bennett


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
752 KB
Volume
158
Category
Article
ISSN
0021-8693

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๐Ÿ“œ SIMILAR VOLUMES


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In the present paper we determine all the elements in the root lattices of symmetrizable KacแސMoody algebras whose reflections preserve the root systems. Also we discuss elements in the root lattices whose reflections preserve the root lattices.

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We give a root multiplicity formula for all the roots of almost hyperbolic Kac-Moody algebras \(H A_{n}^{(1)}\). We use the path realization of crystal bases for the irreducible highest weight modules over quantum affine Lie algebras \(U_{q}\left(A_{n}^{(1)}\right)\) to determine the root multiplici