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Canonical bases for the quantum group of type $A_r$ and piecewise-linear combinatorics
Arkady Berenstein and Andrei Zelevinsky
Source: Duke Math. J. Volume 82, Number 3
(1996), 473-502.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077245250
Mathematical Reviews number (MathSciNet): MR1387682
Zentralblatt MATH identifier: 0898.17006
Digital Object Identifier: doi:10.1215/S0012-7094-96-08221-6
References
[1] K. Baclawski, A new rule for computing Clebsch-Gordan series, Adv. in Appl. Math. 5 (1984), no. 4, 416–432.
Mathematical Reviews (MathSciNet): MR86i:22030
Zentralblatt MATH: 0559.22010
Digital Object Identifier: doi:10.1016/0196-8858(84)90016-2
[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.
Mathematical Reviews (MathSciNet): MR96e:05178
Zentralblatt MATH: 0848.20007
[3] A. Berenstein and A. Zelevinsky, Tensor product multiplicities and convex polytopes in partition space, J. Geom. Phys. 5 (1988), no. 3, 453–472.
Mathematical Reviews (MathSciNet): MR91k:17003
Zentralblatt MATH: 0712.17006
Digital Object Identifier: doi:10.1016/0393-0440(88)90033-2
[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.
Mathematical Reviews (MathSciNet): MR94g:17019
Zentralblatt MATH: 0794.17007
[5] E. R. Gansner, On the equality of two plane partition correspondences, Discrete Math. 30 (1980), no. 2, 121–132.
Mathematical Reviews (MathSciNet): MR81g:05010
Zentralblatt MATH: 0467.05009
Digital Object Identifier: doi:10.1016/0012-365X(80)90114-4
[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.
Zentralblatt MATH: 0606.17006
[7] H. Knight and A. Zelevinsky, Representations of quivers of type A and the multisegment duality, to appear in Adv. Math.
Mathematical Reviews (MathSciNet): MR1371654
Zentralblatt MATH: 0915.16009
Digital Object Identifier: doi:10.1006/aima.1996.0013
[8] G. Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston Inc., Boston, MA, 1993.
Mathematical Reviews (MathSciNet): MR94m:17016
Zentralblatt MATH: 0788.17010
[9] M.-P. Schützenberger, Promotion des morphismes d'ensembles ordonnés, Discrete Math. 2 (1972), 73–94.
Mathematical Reviews (MathSciNet): MR45:8587
Zentralblatt MATH: 0279.06001
Digital Object Identifier: doi:10.1016/0012-365X(72)90062-3
[10] J. R. Stembridge, On minuscule representations, plane partitions and involutions in complex Lie groups, Duke Math. J. 73 (1994), no. 2, 469–490.
Mathematical Reviews (MathSciNet): MR95c:05009
Zentralblatt MATH: 0805.22006
Digital Object Identifier: doi:10.1215/S0012-7094-94-07320-1
Project Euclid: euclid.dmj/1077288819
[11] J. R. Stembridge, Canonical bases and self-evacuating tableaux, Duke Math. J. 82 (1996), no. 3, 585–606.
Mathematical Reviews (MathSciNet): MR97f:05193
Zentralblatt MATH: 0869.17011
Digital Object Identifier: doi:10.1215/S0012-7094-96-08224-1
Project Euclid: euclid.dmj/1077245253
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