Indecomposable parabolic bundles and the existence of matrices in prescribed conjugacy class closures with product equal to the identity
By W. Crawley‐Boevey. 2003
56 citations recorded by the source corpus.
We study the possible dimension vectors of indecomposable parabolic bundles on the projective line, and use our answer to solve the problem of characterizing those collections of conjugacy classes of n by n matrices for which one can find matrices in their closures whose product is equal to the identity matrix. Both answers depend on the root system of a Kac-Moody Lie algebra. Our proofs use Ringel's theory of tubular algebras, work of Mihai on the existence of logarithmic connections, the Riemann-Hilbert correspondence and an algebraic version, due to Dettweiler and Reiter, of Katz's middle convolution operation.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/65781e91a240d8d5e3a706e965214e5ec3d69ede
How researchers see this paper
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In Algebra and Number Theory
In Geometry and Topology
- Tamás Hausel
- Fernando Rodriguez-Villegas
- E. Letellier
- Stefan Reiter
- Michael Dettweiler
- O. Schiffmann
- Zhiwei Yun
- Anton Mellit
Citations in the corpus
- Arithmetic harmonic analysis on character and quiver varieties II (2008, background): “Following [2] we say that a dimension vector v of Γ is strict if for each i = 1, .”
- Middle convolution of Fuchsian systems and the construction of rigid differential systems (2007, methodology): “Using MCλ, Crawley-Boevey [3] gives a direct criterion (in terms of the Jordan canonical forms) for the existence of linearly rigid tuples.”
- Katz's middle convolution algorithm (2006, unknown): “A G ] 2 5 O ct”