✦ LIBER ✦
Borel Subalgebras and Categories of Highest Weight Modules for Toroidal Lie Algebras
✍ Scribed by B Cox; V Futorny
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 220 KB
- Volume
- 236
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
In this article we begin an investigation of the conjugacy classes of Borel subalgebras together with Verma modules induced from ''standard'' Borel subalgebras of a toroidal Lie algebra ᒑ in two variables. We define, for each highest weight , a category O O of representations of ᒑ that contain these Verma modules and show that when a certain central element acts nontrivially this category is equiva-Ž . lent to the category O O ᒊ for an extension of a suitable affine Kac᎐Moody algebra ᒊ ; ᒑ. From this equivalence we obtain a BGG type resolution and BGG duality theorem in the setting of O O .