## Duke Mathematical Journal

### Canonical bases and self-evacuating tableaux

John R. Stembridge

#### Article information

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

Dates
First available in Project Euclid: 19 February 2004

http://projecteuclid.org/euclid.dmj/1077245253

Digital Object Identifier
doi:10.1215/S0012-7094-96-08224-1

Mathematical Reviews number (MathSciNet)
MR1387685

Zentralblatt MATH identifier
0869.17011

#### Citation

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. http://projecteuclid.org/euclid.dmj/1077245253.

#### References

• [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.