Quantum groups and fusion rules multiplicities

We perform explicitly a truncation of the tensor product of two regular representations of U q(g) for q a root of unity and show that it coincides with the fusion rules for integrable representations in a WZW theory based on the affine Lie algebra g (1). We obtain a new formula for the multiplicitie...

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Bibliographic Details
Published in:Nuclear physics. B 1990-10, Vol.343 (1), p.205-227
Main Authors: Furlan, P., Ganchev, A.Ch, Petkova, V.B.
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Physics
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Summary:We perform explicitly a truncation of the tensor product of two regular representations of U q(g) for q a root of unity and show that it coincides with the fusion rules for integrable representations in a WZW theory based on the affine Lie algebra g (1). We obtain a new formula for the multiplicities which may be useful in practical calculations and which generalizes a classical formula of Weyl.
ISSN:0550-3213
1873-1562
DOI:10.1016/0550-3213(90)90601-9