Generating-function method for tensor products
| Autor: | L. Bégin, Pierre Mathieu, C. Cummins |
|---|---|
| Rok vydání: | 2000 |
| Předmět: |
High Energy Physics - Theory
010308 nuclear & particles physics Computer science Diophantine equation 010102 general mathematics Generating function FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) 01 natural sciences Algebra Set (abstract data type) Tensor product Character (mathematics) High Energy Physics - Theory (hep-th) 0103 physical sciences Lie algebra Fusion rules Affine transformation 0101 mathematics Mathematical Physics |
| Zdroj: | Journal of Mathematical Physics. 41:7611-7639 |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/1.1286511 |
| Popis: | This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp's character method. An alternative approach to the construction of tensor-product generating functions is then presented which overcomes most of the technical difficulties associated with the character method. It is based on the reformulation of the problem of calculating tensor products in terms of the solution of a set of linear and homogeneous Diophantine equations whose elementary solutions represent ``elementary couplings''. Grobner bases provide a tool for generating the complete set of relations between elementary couplings and, most importantly, as an algorithm for specifying a complete, compatible set of ``forbidden couplings''. Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced version of hep-th/9811113 (with new title); to appear in J. Math. Phys |
| Databáze: | OpenAIRE |
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