JP Journal of Algebra, Number Theory and Applications
Volume 27, Issue 2, Pages 193 - 201
(December 2012)
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A PARTICULAR CASE OF THE LEVEL INCREASING PROPERTY
Omar Saldarriaga
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Abstract: Fusion algebras were defined by Fuchs, see [8], and a wide class of examples were found in the representation theory of affine Lie algebras, where they appear as a two parameter family with the Lie algebra. It was conjectured for many years that the structure constants for this algebras satisfy the level increasing property which establishes that
for all l, m and n and for all
Recently this conjecture was proved by Feingold and Fredenhagen, see [4], by using algebraic techniques.
In this paper, we give a different proof of a particular case of this level increasing property for type A fusion algebras by using a pure combinatorial argument which involves orbits of which were also introduced by Feingold and his co-author Weiner, see [2]. |
Keywords and phrases: fusionalgebras, fusion coefficients, affine Lie algebra, orbits of
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