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The Kazhdan-Lusztig conjecture for finite W-algebras | | K. de Vos
; P. van Driel
; | | Date: |
3 Dec 1993 | | Journal: | Lett.Math.Phys. 35 (1995) 333-344 | | Subject: | High Energy Physics - Theory; Quantum Algebra | hep-th math.QA | | Abstract: | We study the representation theory of finite W-algebras. After introducing parabolic subalgebras to describe the structure of W-algebras, we define the Verma modules and give a conjecture for the Kac determinant. This allows us to find the completely degenerate representations of the finite W-algebras. To extract the irreducible representations we analyse the structure of singular and subsingular vectors, and find that for W-algebras, in general the maximal submodule of a Verma module is not generated by singular vectors only. Surprisingly, the role of the (sub)singular vectors can be encapsulated in terms of a `dual’ analogue of the Kazhdan-Lusztig theorem for simple Lie algebras. These involve dual relative Kazhdan-Lusztig polynomials. We support our conjectures with some examples, and briefly discuss applications and the generalisation to infinite W-algebras. | | Source: | arXiv, hep-th/9312016 | | Services: | Forum | Review | PDF | Favorites | |
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