Duke Mathematical Journal

Canonical bases for the quantum group of type Ar and piecewise-linear combinatorics

Arkady Berenstein and Andrei Zelevinsky

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 82, Number 3 (1996), 473-502.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077245250

Digital Object Identifier
doi:10.1215/S0012-7094-96-08221-6

Mathematical Reviews number (MathSciNet)
MR1387682

Zentralblatt MATH identifier
0898.17006

Subjects
Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Secondary: 05E10: Combinatorial aspects of representation theory [See also 20C30] 17B10

Citation

Berenstein, Arkady; Zelevinsky, Andrei. Canonical bases for the quantum group of type $A_r$ and piecewise-linear combinatorics. Duke Math. J. 82 (1996), no. 3, 473--502. doi:10.1215/S0012-7094-96-08221-6. https://projecteuclid.org/euclid.dmj/1077245250


Export citation

References

  • [1] K. Baclawski, A new rule for computing Clebsch-Gordan series, Adv. in Appl. Math. 5 (1984), no. 4, 416–432.
  • [2] A. Berenstein and A. N. Kirillov, Groups generated by involutions, Gelfand-Tsetlin patterns, and combinatorics of Young tableaux, Algebra i Analiz 7 (1995), no. 1, 92–152.
  • [3] A. Berenstein and A. Zelevinsky, Tensor product multiplicities and convex polytopes in partition space, J. Geom. Phys. 5 (1988), no. 3, 453–472.
  • [4] A. Berenstein and A. Zelevinsky, String bases for quantum groups of type $A\sb r$, I. M. Gelfand Seminar, Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 51–89.
  • [5] E. R. Gansner, On the equality of two plane partition correspondences, Discrete Math. 30 (1980), no. 2, 121–132.
  • [6] I. M. Gelfand and A. V. Zelevinsky, Polytopes in the pattern space and canonical bases for irreducible representations of $gl_3$, Funct. Anal. Appl. 19 (1985), 72–75.
  • [7] H. Knight and A. Zelevinsky, Representations of quivers of type A and the multisegment duality, to appear in Adv. Math.
  • [8] G. Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston Inc., Boston, MA, 1993.
  • [9] M.-P. Schützenberger, Promotion des morphismes d'ensembles ordonnés, Discrete Math. 2 (1972), 73–94.
  • [10] J. R. Stembridge, On minuscule representations, plane partitions and involutions in complex Lie groups, Duke Math. J. 73 (1994), no. 2, 469–490.
  • [11] J. R. Stembridge, Canonical bases and self-evacuating tableaux, Duke Math. J. 82 (1996), no. 3, 585–606.