Indecomposable parabolic bundles
Publications Mathématiques de l'IHÉS, Volume 100 (2004), pp. 171-207.

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.

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     author = {Crawley-Boevey, William},
     title = {Indecomposable parabolic bundles},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {171--207},
     publisher = {Springer},
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     year = {2004},
     doi = {10.1007/s10240-004-0025-7},
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     mrnumber = {2102700},
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     url = {http://archive.numdam.org/articles/10.1007/s10240-004-0025-7/}
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Crawley-Boevey, William. Indecomposable parabolic bundles. Publications Mathématiques de l'IHÉS, Volume 100 (2004), pp. 171-207. doi : 10.1007/s10240-004-0025-7. http://archive.numdam.org/articles/10.1007/s10240-004-0025-7/

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