Indecomposable parabolic bundles

William Crawley-Boevey

Publications Mathématiques de l'IHÉS (2004)

  • Volume: 100, page 171-207
  • ISSN: 0073-8301

Abstract

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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×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.

How to cite

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Crawley-Boevey, William. "Indecomposable parabolic bundles." Publications Mathématiques de l'IHÉS 100 (2004): 171-207. <http://eudml.org/doc/104199>.

@article{Crawley2004,
abstract = {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×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.},
author = {Crawley-Boevey, William},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {conjugacy class; Deligne-Simpson problem; root system; Kac-Moody Lie algebra},
language = {eng},
pages = {171-207},
publisher = {Springer},
title = {Indecomposable parabolic bundles},
url = {http://eudml.org/doc/104199},
volume = {100},
year = {2004},
}

TY - JOUR
AU - Crawley-Boevey, William
TI - Indecomposable parabolic bundles
JO - Publications Mathématiques de l'IHÉS
PY - 2004
PB - Springer
VL - 100
SP - 171
EP - 207
AB - 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×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.
LA - eng
KW - conjugacy class; Deligne-Simpson problem; root system; Kac-Moody Lie algebra
UR - http://eudml.org/doc/104199
ER -

References

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