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
@article{PMIHES_2004__100__171_0, author = {Crawley-Boevey, William}, title = {Indecomposable parabolic bundles}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {171--207}, publisher = {Springer}, volume = {100}, year = {2004}, doi = {10.1007/s10240-004-0025-7}, mrnumber = {2102700}, zbl = {1065.14040}, language = {en}, url = {https://www.numdam.org/articles/10.1007/s10240-004-0025-7/} }
TY - JOUR AU - Crawley-Boevey, William TI - Indecomposable parabolic bundles JO - Publications Mathématiques de l'IHÉS PY - 2004 SP - 171 EP - 207 VL - 100 PB - Springer UR - https://www.numdam.org/articles/10.1007/s10240-004-0025-7/ DO - 10.1007/s10240-004-0025-7 LA - en ID - PMIHES_2004__100__171_0 ER -
Crawley-Boevey, William. Indecomposable parabolic bundles. Publications Mathématiques de l'IHÉS, Tome 100 (2004), pp. 171-207. doi : 10.1007/s10240-004-0025-7. https://www.numdam.org/articles/10.1007/s10240-004-0025-7/
1. Eigenvalues of products of unitary matrices and quantum Schubert calculus, Math. Res. Lett., 5 (1998), 817-836. | MR | Zbl
and ,2. Complex analytic connections in fibre bundles, Trans. Am. Math. Soc., 85 (1957), 181-207. | MR | Zbl
,3. Local systems on P 1-S for S a finite set, Compos. Math., 129 (2001), 67-86. | MR | Zbl
,4. A criterion for the existence of a flat connection on a parabolic vector bundle, Adv. Geom., 2 (2002), 231-241. | MR | Zbl
,5. Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors, Representation Theory II (Ottawa, 1979), V. Dlab and P. Gabriel (eds.), Lect. Notes Math., 832, Springer, Berlin (1980), 103-169. | MR | Zbl
and ,6. Non-commutative coordinate rings and stacks, Proc. London Math. Soc., 88 (2004), 63-88. | MR | Zbl
and ,7. Geometry of the moment map for representations of quivers, Compos. Math., 126 (2001), 257-293. | MR | Zbl
,8. Normality of Marsden-Weinstein reductions for representations of quivers, Math. Ann., 325 (2003), 55-79. | MR | Zbl
,9. On matrices in prescribed conjugacy classes with no common invariant subspace and sum zero, Duke Math. J., 118 (2003), 339-352. | MR | Zbl
,10. Irreducible components of varieties of modules, J. Reine Angew. Math., 553 (2002), 201-220. | MR | Zbl
and ,11. Equations différentielles à points singuliers réguliers, Lect. Notes Math., 163, Springer, Berlin (1970). | MR | Zbl
,12. An algorithm of Katz and its application to the inverse Galois problem, J. Symb. Comput., 30 (2000), 761-798. | MR | Zbl
and ,13. Seifert fibred homology 3-spheres and the Yang-Mills equations on Riemann surfaces with marked points, Adv. Math., 96 (1992), 38-102. | MR | Zbl
and ,14. A class of weighted projective curves arising in representation theory of finite dimensional algebras, Singularities, representations of algebras, and vector bundles (Lambrecht, 1985), G.-M. Greuel and G. Trautmann (eds.), Lect. Notes Math., 1273, Springer, Berlin (1987), 265-297. | MR | Zbl
and ,15. On nilalgebras and linear varieties of nilpotent matrices, III, Ann. Math., 70 (1959), 167-205. | MR | Zbl
,16. A. Haefliger, Local theory of meromorphic connections in dimension one (Fuchs theory), chapter III of A. Borel et al., Algebraic D-modules, Acad. Press, Boston (1987), 129-149.
17. Tilting in abelian categories and quasitilted algebras, Mem. Am. Math. Soc., 120, no. 575 (1996). | MR | Zbl
, and ,18. Infinite root systems, representations of graphs and invariant theory, Invent. Math., 56 (1980), 57-92. | MR | Zbl
,19. Root systems, representations of quivers and invariant theory, Invariant theory (Montecatini, 1982), F. Gherardelli (ed.), Lect. Notes Math., 996, Springer, Berlin (1983), 74-108. | MR | Zbl
,20. Rigid local systems, Princeton University Press, Princeton, NJ (1996). | MR | Zbl
,21. On the existence of monodromy groups of Fuchsian systems on Riemann's sphere with unipotent generators, J. Dynam. Control Systems, 2 (1996), 125-155. | Zbl
,22. On the Deligne-Simpson problem, C. R. Acad. Sci., Paris, Sér. I, Math., 329 (1999), 657-662. | MR | Zbl
,23. On some aspects of the Deligne-Simpson problem, J. Dynam. Control Systems, 9 (2003), 393-436. | MR | Zbl
,24. The Deligne-Simpson problem - a survey, preprint math.RA/0206298. | MR | Zbl
,25. Geometry of representations of quivers, Representations of algebras (Durham, 1985), P. Webb (ed.) Lond. Math. Soc. Lect. Note Ser., 116, Cambridge Univ. Press (1986), 109-145. | MR | Zbl
and ,26. Representations of finite dimensional algebras and singularity theory, Trends in ring theory (Miskolc, Hungary, 1996), Canadian Math. Soc. Conf. Proc., 22 (1998), Am. Math. Soc., Providence, RI (1998), 71-97. | MR | Zbl
,27. B. Malgrange, Regular connections, after Deligne, chapter IV of A. Borel et al., Algebraic D-modules, Acad. Press, Boston (1987), 151-172.
28. Moduli of vector bundles on curves with parabolic structure, Math. Ann., 248 (1980), 205-239. | MR | Zbl
and ,29. Sheaves on a weighted projective line of genus one, and representations of a tubular algebra, Representations of algebras (Ottawa, 1992), Can. Math. Soc. Conf. Proc., 14 (1993), Am. Math. Soc., Providence, RI (1993), 313-337. | MR | Zbl
and ,30. Sur le résidue et la monodromie d'une connexion méromorphe, C. R. Acad. Sci., Paris, Sér. A, 281 (1975), 435-438. | Zbl
,31. Sur les connexions méromorphes, Rev. Roum. Math. Pures Appl., 23 (1978), 215-232. | MR | Zbl
,32. Singular regular differential equations and eigenvalues of products of matrices, Linear Multilinear Algebra, 46 (1999), 145-164. | MR | Zbl
and ,33. Tame algebras and integral quadratic forms, Lect. Notes Math., 1099, Springer, Berlin (1984). | MR | Zbl
,34. Matrices and cohomology, Ann. Math., 105 (1977), 473-492. | MR | Zbl
,35. Fibrés vectoriels sur les courbes algébriques, Astérisque, 98 (1982), 1-209. | Numdam | MR | Zbl
,36. Products of Matrices, Differential geometry, global analysis, and topology (Halifax, NS, 1990), Can. Math. Soc. Conf. Proc., 12 (1992), Am. Math. Soc., Providence, RI (1991), 157-185. | MR | Zbl
,37. On linearly rigid tuples, J. Reine Angew. Math., 510 (1999), 57-62. | MR | Zbl
and ,38. The braid group and linear rigidity, Geom. Dedicata, 84 (2001), 135-150. | MR | Zbl
,39. Generalization de fonctions abeliennes, J. Math. Pures Appl., 17 (1938), 47-87. | JFM
,- Low-dimensional quadratic relative character varieties for the projective line minus three points, Science China Mathematics (2024) | DOI:10.1007/s11425-024-2330-8
- Intersection cohomology of character varieties for punctured Riemann surfaces, Journal de l’École polytechnique — Mathématiques, Volume 10 (2023), p. 141 | DOI:10.5802/jep.215
- Finite-dimensional irreducible modules of the universal DAHA of type (C1∨,C1), Linear and Multilinear Algebra, Volume 70 (2022) no. 15, p. 2856 | DOI:10.1080/03081087.2020.1817297
- Symplectic Resolutions for Multiplicative Quiver Varieties and Character Varieties for Punctured Surfaces, Representation Theory and Algebraic Geometry (2022), p. 393 | DOI:10.1007/978-3-030-82007-7_9
- Topological generation of special linear groups, Journal of Algebra, Volume 569 (2021), p. 511 | DOI:10.1016/j.jalgebra.2020.10.020
- Moduli of regular singular parabolic connections with given spectral type on smooth projective curves, Journal of the Mathematical Society of Japan, Volume 70 (2018) no. 3 | DOI:10.2969/jmsj/76597659
- Goursat rigid local systems of rank four, Research in the Mathematical Sciences, Volume 5 (2018) no. 4 | DOI:10.1007/s40687-018-0156-y
- Global Weyl groups and a new theory of multiplicative quiver varieties, Geometry Topology, Volume 19 (2016) no. 6, p. 3467 | DOI:10.2140/gt.2015.19.3467
- On Galois action in rigid DAHA modules, International Mathematics Research Notices (2016), p. rnw034 | DOI:10.1093/imrn/rnw034
- On Weyl groups and Artin groups associated to orbifold projective lines, Journal of Algebra, Volume 453 (2016), p. 249 | DOI:10.1016/j.jalgebra.2015.12.016
- PARABOLIC BUNDLES OVER THE PROJECTIVE LINE AND THE DELIGNE–SIMPSON PROBLEMS, The Quarterly Journal of Mathematics, Volume 67 (2016) no. 1, p. 75 | DOI:10.1093/qmath/hav041
- Character varieties with Zariski closures of
GL n -conjugacy classes at punctures, Selecta Mathematica, Volume 21 (2015) no. 1, p. 293 | DOI:10.1007/s00029-014-0163-9 - CONNECTIONS ON REAL PARABOLIC BUNDLES OVER A REAL CURVE, Bulletin of the Korean Mathematical Society, Volume 51 (2014) no. 4, p. 1101 | DOI:10.4134/bkms.2014.51.4.1101
- Arithmetic harmonic analysis on character and quiver varieties II, Advances in Mathematics, Volume 234 (2013), p. 85 | DOI:10.1016/j.aim.2012.10.009
- An example of the Langlands correspondence for irregular rank two connections on P1, Advances in Mathematics, Volume 230 (2012) no. 3, p. 1078 | DOI:10.1016/j.aim.2012.03.003
- FURTHER GEOMETRIC RESTRICTIONS ON JORDAN STRUCTURE IN MATRIX FACTORIZATION, Asian-European Journal of Mathematics, Volume 05 (2012) no. 02, p. 1250018 | DOI:10.1142/s1793557112500180
- Arithmetic harmonic analysis on character and quiver varieties, Duke Mathematical Journal, Volume 160 (2011) no. 2 | DOI:10.1215/00127094-1444258
- Complex Lie algebras corresponding to weighted projective lines, Frontiers of Mathematics in China, Volume 6 (2011) no. 4, p. 629 | DOI:10.1007/s11464-010-0070-0
- Connections for weighted projective lines, Journal of Pure and Applied Algebra, Volume 215 (2011) no. 1, p. 35 | DOI:10.1016/j.jpaa.2010.02.030
- Middle convolution and Harnad duality, Mathematische Annalen, Volume 349 (2011) no. 1, p. 215 | DOI:10.1007/s00208-010-0517-3
- Geometry of Multiplicative Preprojective Algebra, International Mathematics Research Papers (2010) | DOI:10.1093/imrp/rpn008
- Holomorphic vector bundles on Sasakian threefolds and parabolic vector bundles, Journal of Mathematical Physics, Volume 51 (2010) no. 6 | DOI:10.1063/1.3442721
- Spectrally arbitrary, nonderogatory factorization over a general field, Linear Algebra and its Applications, Volume 433 (2010) no. 1, p. 1 | DOI:10.1016/j.laa.2010.01.029
- Triangulated categories of matrix factorizations for regular systems of weights with ε=−1, Advances in Mathematics, Volume 220 (2009) no. 5, p. 1602 | DOI:10.1016/j.aim.2008.11.001
- Middle convolution of Fuchsian systems and the construction of rigid differential systems, Journal of Algebra, Volume 318 (2007) no. 1, p. 1 | DOI:10.1016/j.jalgebra.2007.08.029
- Multiplicative preprojective algebras, middle convolution and the Deligne–Simpson problem, Advances in Mathematics, Volume 201 (2006) no. 1, p. 180 | DOI:10.1016/j.aim.2005.02.003
- Canonical bases and moduli spaces of sheaves on curves, Inventiones mathematicae, Volume 165 (2006) no. 3, p. 453 | DOI:10.1007/s00222-005-0495-3
- Generalized double affine Hecke algebras of higher rank, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2006 (2006) no. 600 | DOI:10.1515/crelle.2006.091
Cité par 28 documents. Sources : Crossref