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Absolutely indecomposable representations and Kac-Moody Lie algebras

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Abstract

A conjecture of Kac states that the polynomial counting the number of absolutely indecomposable representations of a quiver over a finite field with given dimension vector has positive coefficients and furthermore that its constant term is equal to the multiplicity of the corresponding root in the associated Kac-Moody Lie algebra. In this paper we prove these conjectures for indivisible dimension vectors.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    William Crawley-Boevey

  2. Departement WNI, Limburgs Universitair Centrum, 3590, Diepenbeek, Belgium

    Michel Van den Bergh

Authors
  1. William Crawley-Boevey
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  2. Michel Van den Bergh
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Corresponding authors

Correspondence to William Crawley-Boevey or Michel Van den Bergh.

Additional information

Dedicated to Idun Reiten on the occasion of her sixtieth birthday

Mathematics Subject Classification (1991)

16G20, 17B67

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Crawley-Boevey, W., Van den Bergh, M. Absolutely indecomposable representations and Kac-Moody Lie algebras. Invent. math. 155, 537–559 (2004). https://doi.org/10.1007/s00222-003-0329-0

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  • DOI: https://doi.org/10.1007/s00222-003-0329-0

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