Duke Mathematical Journal

Canonical bases and self-evacuating tableaux

John R. Stembridge

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

Duke Math. J., Volume 82, Number 3 (1996), 585-606.

First available in Project Euclid: 19 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]
Secondary: 05E10: Combinatorial aspects of representation theory [See also 20C30] 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]


Stembridge, John R. Canonical bases and self-evacuating tableaux. Duke Math. J. 82 (1996), no. 3, 585--606. doi:10.1215/S0012-7094-96-08224-1. https://projecteuclid.org/euclid.dmj/1077245253

Export citation


  • [BZ] A. Berenstein and A. Zelevinsky, Canonical bases for the quantum group of type $A\sb r$ and piecewise-linear combinatorics, Duke Math. J. 82 (1996), no. 3, 473–502.
  • [B] N. Bourbaki, Lie groups and Lie algebras. Chapters 1–3, Elements of Mathematics, Springer-Verlag, Berlin, 1989.
  • [CL] C. Carré and B. Leclerc, Splitting the square of a Schur function into its symmetric and antisymmetric parts, J. Algebraic Combin. 4 (1995), no. 3, 201–231.
  • [G] E. R. Gansner, On the equality of two plane partition correspondences, Discrete Math. 30 (1980), no. 2, 121–132.
  • [GM] A. M. Garsia and T. J. McLarnan, Relations between Young's natural and the Kazhdan-Lusztig representations of $S\sb n$, Adv. in Math. 69 (1988), no. 1, 32–92.
  • [Gr] J. Graham, Modular representations of Hecke algebras and related algebras, Ph.D. thesis, University of Sydney, 1995.
  • [GL] I. Grojnowski and G. Lusztig, On bases of irreducible representations of quantum $\rm GL\sb n$, Kazhdan-Lusztig theory and related topics (Chicago, IL, 1989), Contemp. Math., vol. 139, Amer. Math. Soc., Providence, RI, 1992, pp. 167–174.
  • [H] J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, New York, 1972.
  • [JK] G. James and A. Kerber, The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, vol. 16, Addison-Wesley Publishing Co., Reading, Mass., 1981.
  • [Ka] V. G. Kac, Infinite-dimensional Lie algebras, Cambridge University Press, Cambridge, 1990.
  • [KL] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184.
  • [KLLT] A. N. Kirillov, A. Lascoux, B. Leclerc, and J.-Y. Thibon, Séries génératrices pour les tableaux de dominos, C. R. Acad. Sci. Paris Sér. I Math. 318 (1994), no. 5, 395–400.
  • [K] D. E. Knuth, The art of computer programming. Volume 3, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1973.
  • [Ko] B. Kostant, On Macdonald's $\eta$-function formula, the Laplacian and generalized exponents, Advances in Math. 20 (1976), no. 2, 179–212.
  • [Ku] G. Kuperberg, Self-complementary plane partitions by Proctor's minuscule method, European J. Combin. 15 (1994), no. 6, 545–553.
  • [L] G. Lusztig, Canonical bases arising from quantized enveloping algebras. II, Progr. Theoret. Phys. Suppl. (1990), no. 102, 175–201 (1991).
  • [M] I. G. Macdonald, Symmetric functions and Hall polynomials, The Clarendon Press Oxford University Press, New York, 1979.
  • [Mth] A. Mathas, On the left-cell representations of Iwahori-Hecke algebras of finite Coxeter groups, preprint.
  • [Sh] J. Y. Shi, The Kazhdan-Lusztig cells in certain affine Weyl groups, Lecture Notes in Mathematics, vol. 1179, Springer-Verlag, Berlin, 1986.
  • [St] R. P. Stanley, Symmetries of plane partitions, J. Combin. Theory Ser. A 43 (1986), no. 1, 103–113.
  • [SW] D. W. Stanton and D. E. White, A Schensted algorithm for rim hook tableaux, J. Combin. Theory Ser. A 40 (1985), no. 2, 211–247.
  • [Ste] J. R. Stembridge, On minuscule representations, plane partitions and involutions in complex Lie groups, Duke Math. J. 73 (1994), no. 2, 469–490.
  • [vL] M. A. A. van Leeuwen, The Robinson-Schensted and Schützenberger Algorithms Part I: New Combinatorial Proofs, 1992, CWI Technical Report AM-R9208.