Indecomposable parabolic bundles
Publications Mathématiques de l'IHÉS, Volume 100 (2004), p. 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.

@article{PMIHES_2004__100__171_0,
     author = {Crawley-Boevey, William},
     title = {Indecomposable parabolic bundles},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Springer},
     volume = {100},
     year = {2004},
     pages = {171-207},
     doi = {10.1007/s10240-004-0025-7},
     zbl = {1065.14040},
     mrnumber = {2102700},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2004__100__171_0}
}
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://www.numdam.org/item/PMIHES_2004__100__171_0/

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