Dual Pairs and Tensor Categories of Modules over Lie Algebrasgl̂∞and W1 + ∞
✍ Scribed by Weiqiang Wang
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 137 KB
- Volume
- 216
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
We introduce a tensor category O O resp. O O of certain modules of gl with q y ϱ Ž . nonnegative resp. nonpositive integral central charges with the usual tensor Ž . product. We also introduce a tensor category O O , ᭪ consisting of certain modules f Ž . over GL N for all N. We show that the tensor categories O O and O O are " f semisimple abelian and all equivalent to each other. We give a formula to decompose a tensor product of two modules and obtain a reciprocity law in each of these categories. We also introduce a tensor category O O w of certain modules over W W with nonnegative integral central charges. We show that O O w is semisimple 1q ϱ abelian and give an explicit formula to decompose a tensor product of two modules in O O w .