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Kac's conjecture from Nakajima quiver varieties

Abstract:
We prove a generating function formula for the Betti numbers of Nakajima quiver varieties. We prove that it is a q-deformation of the Weyl-Kac character formula. In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a a certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982.
Publication status:
Published

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Publisher copy:
10.1007/s00222-010-0241-3

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
INVENTIONES MATHEMATICAE More from this journal
Volume:
181
Issue:
1
Pages:
21-37
Publication date:
2008-11-10
DOI:
EISSN:
1432-1297
ISSN:
0020-9910
Language:
English
Keywords:
Pubs id:
pubs:58647
UUID:
uuid:fbfe6770-9a22-453e-97ec-bae3affcdc41
Local pid:
pubs:58647
Source identifiers:
58647
Deposit date:
2012-12-19

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