Skip to main content
Log in

Canonical bases and moduli spaces of sheaves on curves

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Ariki, S.: On the decomposition numbers of the Hecke algebra of G(m,1,n). J. Math. Kyoto Univ. 36, 789–808 (1996)

    MATH  MathSciNet  Google Scholar 

  2. Ariki, S.: Representations of Quantum Algebras and Combinatorics of Young Tableaux. Univ. Lect. Ser., vol. 26. Am. Math. Soc. 2002

  3. Beck, J.: Braid group action and quantum affine algebras. Commun. Math. Phys. 165, 555–568 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Beillinson, A., Bernstein, I., Deligne, P.: Faisceaux pervers. Astérisque 100, 5–171 (1982)

    Google Scholar 

  5. Bernstein, J., Lunts, V.: Equivariant Sheaves and Functors. Lect. Notes Math., vol. 1578. Springer 1994

  6. Biswas, I.: Parabolic bundles as orbifold bundles. Duke Math. J. 88, 305–325 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Borho, W., Macpherson, R.: Partial resolutions of nilpotent varieties. Analysis and topology on singular spaces, II, III. Astérisque 101102, 23–74 (1981)

  8. Burban, I., Schiffmann, O.: Hall algebra of an elliptic curve, I. Preprint math.AG/0505148

  9. Caldero, P.: Toric degenerations of Schubert varieties. Transform. Groups 7, 51–60 (2002)

    MATH  MathSciNet  Google Scholar 

  10. Crawley-Boevey, W.: Indecomposable parabolic bundles and the existence of matrices in prescribed conjugacy class closures with product equal to the identity. Publ. Math., Inst. Hautes Étud. Sci. 100, 171–207 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Deligne, P.: La conjecture de Weil II. Publ. Math., Inst. Hautes Étud. Sci. 52, 137–252 (1980)

    MATH  MathSciNet  Google Scholar 

  12. Drinfeld, V.: A new realization of Yangians and quantized affine algebras. Sov. Math. Dokl. 36, 212–216 (1988)

    MATH  MathSciNet  Google Scholar 

  13. Feigin, B., Stoyanovsky, A.: Functional models of the representations of current algebras, and semi-infinite Schubert cells. Funkts. Anal. Prilozh. 28, 68–90, 96 (1994)

    MATH  MathSciNet  Google Scholar 

  14. Fomin, S., Zelevinsky, A.: Cluster algebras. I. Foundations. J. Am. Math. Soc. 15, 497–529 (2002)

    Article  MATH  Google Scholar 

  15. Geigle, W., Lenzing, H.: A class of weighted projective curves arising in the representation theory of finite-dimensional algebras. Singularities, representations of algebras and vector bundles, Lect. Notes Math, vol. 1273, pp. 265–297. Springer 1987

  16. Grothendieck, A.: Techniques de constructions et théorèmes d’existence en géométrie algébrique IV: les schémas de Hilbert. Sém. Bourbaki 221 (1960–1961)

  17. Hartshorne, R.: Algebraic Geometry. Springer 1977

  18. Hubery, A.: Three presentations of the Hopf algebra \(\mathcal{U}_v(\widehat{\mathfrak{gl}}_n)\). Preprint

  19. Jimbo, M., Misra, K., Miwa, T., Okado, M.: Combinatorics of representations of \(U_q(\widehat{\mathfrak{sl}}(n))\) at q=0. Commun. Math. Phys. 136, 543–566 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  20. Kashiwara, M.: On crystal bases of the Q-analogue of universal enveloping algebras. Duke Math. J. 63, 465–516 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  21. Kapranov, M.: Eisenstein series and quantum affine algebras. Algebraic geometry, 7. J. Math. Sci., New York 84, 1311–1360 (1997)

  22. Kashiwara, M., Miwa, T., Stern, E.: Decomposition of q-deformed Fock spaces. Sel. Math. 1, 787–805 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  23. Kiehl, R., Weissauer, R.: Weil conjectures, perverse sheaves and l’adic Fourier transform. Ergeb. Math. Grenzgeb., vol. 42. Springer 2001

  24. Lascoux, A., Leclerc, B., Thibon, J.-Y.: Hecke algebras at roots of unity and crystal bases of quantum affine algebras. Commun. Math. Phys. 181, 205–263 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  25. Laumon, G.: Faisceaux automorphes liés aux séries d’Eisenstein. In: Automorphic Forms, Shimura Varieties and L-functions. Perspect. Math., vol. 10, pp. 227–279. Boston: Academic Press 1990

  26. Laumon, G., Moret-Bailly, L.: Champs Algébriques. Ergeb. Math. Grenzgeb. 3. Folge, vol. 39. Springer 2000

  27. Lenzing, H.: Curve singularities arising from the representation theory of tame hereditary algebras. Representation Theory, I (Ottawa, Canada 1984), Lect. Notes Math., vol. 1177, pp. 199–231. Springer 1986

  28. Lenzing, H., Meltzer, H.: Sheaves on a weighted projective line of genus one, and representations of a tubular algebra. Representations of Algebras (Ottawa, Canada 1992), CMS Conf. Proc., vol. 14, pp. 313–337, 1993

  29. Le Potier, J.: Fibrés vectoriels sur les courbes algébriques. Publ. Math. Univ. Paris VII (1996)

  30. Lusztig, G.: Introduction to quantum groups. Birkhäuser 1992

  31. Lusztig, G.: Quivers, perverse sheaves and quantized enveloping algebras. J. Am. Math. Soc. 4, 365–421 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  32. Lusztig, G.: Canonical bases and Hall algebras. Representation theories and algebraic geometry (Montréal 1997). NATO ASI Ser., Ser. C, Math. Phys. Sci. 514, 365–399 (1998)

  33. Lusztig, G.: Affine quivers and canonical bases. Publ. Math., Inst. Hautes Étud. Sci. 76, 111–163 (1992)

    MATH  MathSciNet  Google Scholar 

  34. McGerty, K.: The Kronecker quiver and bases of quantum affine \(\mathfrak{sl}_2\). Adv. Math. 197, 411–429 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  35. Moody, R., Rao, E., Yokonuma, T.: Toroidal Lie algebras and vertex representations. Geom. Dedicata 35, 283–307 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  36. Ringel, C.: Hall algebras and quantum groups. Invent. Math. 101, 583–591 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  37. Saito, K., Yoshii, D.: Extended affine root system. IV. Simply-laced elliptic Lie algebras. Publ. Res. Inst. Math. Sci. 36, 385–421 (2000)

    MATH  Google Scholar 

  38. Schiffmann, O.: The Hall algebra of a cyclic quiver and canonical bases of Fock spaces. Int. Math. Res. Not. 8, 413–440 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  39. Schiffmann, O.: Noncommutative projective curves and quantum loop algebras. Duke Math. J. 121, 113–168 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  40. Schiffmann, O.: On the Hall algebra of an elliptic curve, II. Preprint math.RT/0508553 (2005)

  41. Varagnolo, M., Vasserot, E.: On the decomposition matrices of the quantized Schur algebra. Duke Math. J. 100, 267–297 (1999)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Olivier Schiffmann.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schiffmann, O. Canonical bases and moduli spaces of sheaves on curves. Invent. math. 165, 453–524 (2006). https://doi.org/10.1007/s00222-005-0495-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00222-005-0495-3

Keywords

Navigation