Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Kazhdan-Lusztig conjecture for finite W-algebras   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.

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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph