Jones–Witten Invariants for Nonsimply Connected Lie Groups and the Geometry of the Weyl Alcove
✍ Scribed by Stephen F. Sawin
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 310 KB
- Volume
- 165
- Category
- Article
- ISSN
- 0001-8708
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✦ Synopsis
The quotient process of Mu ger and BruguieÁ res is used to construct modular categories and TQFTs out of closed subsets of the Weyl alcove of a simple Lie algebra. In particular it is determined at which levels closed subsets associated to nonsimply connected groups lead to TQFTs. Many of these TQFTs are shown to decompose into a tensor product of TQFTs coming from smaller subsets. The ``prime'' subsets among these are classified, and apart from some giving TQFTs depending on homology as described by Murakami, Ohtsuki and Okada, they are shown to be in one-to-one correspondence with the TQFTs predicted by Dijkgraaf and Witten to be associated to Chern Simons theory with a nonsimply connected Lie group. Thus in particular a rigorous construction of the Dijkgraaf Witten TQFTs is given. As a byproduct, a purely quantum groups proof of the modularity of the full Weyl alcove for arbitrary quantum groups at arbitrary levels is given.