Duke Mathematical Journal

On the decomposition matrices of the quantized Schur algebra

Michela Varagnolo and Eric Vasserot

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 100, Number 2 (1999), 267-297.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077227354

Digital Object Identifier
doi:10.1215/S0012-7094-99-10010-X

Mathematical Reviews number (MathSciNet)
MR1722955

Zentralblatt MATH identifier
0962.17006

Subjects
Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Secondary: 20C08: Hecke algebras and their representations

Citation

Varagnolo, Michela; Vasserot, Eric. On the decomposition matrices of the quantized Schur algebra. Duke Math. J. 100 (1999), no. 2, 267--297. doi:10.1215/S0012-7094-99-10010-X. http://projecteuclid.org/euclid.dmj/1077227354.


Export citation

References

  • [A] Susumu Ariki, On the decomposition numbers of the Hecke algebra of $G(m,1,n)$, J. Math. Kyoto Univ. 36 (1996), no. 4, 789–808.
  • [ChP] Vyjayanthi Chari and Andrew Pressley, A guide to quantum groups, Cambridge University Press, Cambridge, 1994.
  • [D] Vinay V. Deodhar, On some geometric aspects of Bruhat orderings. II. The parabolic analogue of Kazhdan-Lusztig polynomials, J. Algebra 111 (1987), no. 2, 483–506.
  • [Du] Jie Du, A note on quantized Weyl reciprocity at roots of unity, Algebra Colloq. 2 (1995), no. 4, 363–372.
  • [GiV] Victor Ginzburg and Éric Vasserot, Langlands reciprocity for affine quantum groups of type $A\sb n$, Internat. Math. Res. Notices (1993), no. 3, 67–85.
  • [G] James A. Green, Hall algebras, hereditary algebras and quantum groups, Invent. Math. 120 (1995), no. 2, 361–377.
  • [Gr] R. M. Green, The affine $q$-Schur algebra, available from http://xxx.lanl.gov/abs/q-alg/9705015.
  • [H] Takahiro Hayashi, $q$-analogues of Clifford and Weyl algebras—spinor and oscillator representations of quantum enveloping algebras, Comm. Math. Phys. 127 (1990), no. 1, 129–144.
  • [IMa] N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of ${\germ p}$-adic Chevalley groups, Inst. Hautes Études Sci. Publ. Math. (1965), no. 25, 5–48.
  • [KMS] M. Kashiwara, T. Miwa, and E. Stern, Decomposition of $q$-deformed Fock spaces, Selecta Math. (N.S.) 1 (1995), no. 4, 787–805.
  • [KT] Masaki Kashiwara and Toshiyuki Tanisaki, Kazhdan-Lusztig conjecture for affine Lie algebras with negative level, Duke Math. J. 77 (1995), no. 1, 21–62.
  • [KaL]1 D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. I, II, J. Amer. Math. Soc. 6 (1993), no. 4, 905–947, 949–1011.
  • [KaL]2 D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. III, J. Amer. Math. Soc. 7 (1994), no. 2, 335–381.
  • [KaL]3 D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. IV, J. Amer. Math. Soc. 7 (1994), no. 2, 383–453.
  • [LeTh] Bernard Leclerc and Jean-Yves Thibon, Canonical bases of $q$-deformed Fock spaces, Internat. Math. Res. Notices (1996), no. 9, 447–456.
  • [L1] G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), no. 2, 447–498.
  • [L2] G. Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4 (1991), no. 2, 365–421.
  • [L3] George Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston Inc., Boston, MA, 1993.
  • [L4] George Lusztig, Canonical bases and Hall algebras, Representation theories and algebraic geometry (Montreal, PQ, 1997), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 514, Kluwer Acad. Publ., Dordrecht, 1998, pp. 365–399.
  • [MiM] Kailash Misra and Tetsuji Miwa, Crystal base for the basic representation of $U\sb q(\germ s\germ l(n))$, Comm. Math. Phys. 134 (1990), no. 1, 79–88.
  • [N] Hiraku Nakajima, Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras, Duke Math. J. 76 (1994), no. 2, 365–416.
  • [Sch] Olivier Schiffmann, Algèbres affines quantiques aux racines de l'unité et $K$-théorie équivariante, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), no. 5, 433–438.
  • [VaV] M. Varagnolo and E. Vasserot, Double-loop algebras and the Fock space, Invent. Math. 133 (1998), no. 1, 133–159.
  • [V1] Éric Vasserot, Représentations de groupes quantiques et permutations, Ann. Sci. École Norm. Sup. (4) 26 (1993), no. 6, 747–773.
  • [V2] E. Vasserot, Affine quantum groups and equivariant $K$-theory, Transform. Groups 3 (1998), no. 3, 269–299.