Noncommutative Symmetric Functions V: A Degenerate Version of Uq(glN)

International Journal of Algebra and Computation

Volumn 9, Issue 3-4, 1999, Pages 405-430

  Krob, Daniel ^a   Thibon, Jean Yves ^b  

^a UNIVERSITÉ PARIS DIDEROT   (France)

^b UNIVERSITÉ GUSTAVE EIFFEL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033407263     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0218196799000254     Document Type: Article

References (35)

1. S. Ariki, On the decomposition numbers of the Hecke algebra ofG(m, 1, n), J. Math. Kyoto University 36 (1996), 789-808.
2. J. Berstel and G. Reutenauer, Les séries rationnelles et leurs langages, Masson, 1984.
3. R. W. Carter, Representation theory of the 0-Hecke algebra, J. Algebra, 15 (1986), 89-103.
4. N) at q = 0 and the Robinson-Schensted correspondence, in Physics and mathematics of strings, Memorial volume of V. Knizhnik, eds. L. Brink, D. Friedans and A. M. Polyakov, World Scientific, 1990.
5. n, Proc. London Math. Soc. 63 (1991), 165-211.
6. R. Dipper James, Blocks and idempotents of Hecke algebras of general linear groups, Proc. London Math. Soc. 54 (1987), 57-82.
7. G. Duchamp, A. Klyachko, D. Krob and J.-Y. Thibon, Noncommutative symmetric functions III: Deformations of Cauchy and convolution algebras, Discrete Math, and Theor. Comput. Sci. 1 (1997), 159-216.
8. G. Duchamp, D. Krob, A. Lascoux, B. Leclerc, T. Scharf and J.-Y. Thibon, Euler-Poincaré characteristic and polynomial representations of Iwahori-Hecke algebras, Publ. RIMS, Kyoto University 31 (1995), 179-201.
9. G. Duchamp, D. Krob, B. Leclerc and J-Y. Thibon, Fonctions quasi-symétriques, fonctions symétriques noncommutatives, et algèbres de Hecke à q = 0, C.R. Acad. Sci. Paris 322 (1996), 107-112.
10. L. D. Faddeev, N. Y. Reshetikin and L. A. Takhtadzhyan, Quantization of Lie groups and Lie algebras, Leningrad Math. J. 1 (1990), 193-225.
11. I. M. Gelfand, D. Krob, B. Leclerc, A. Lascoux, V. S. Retakh and J.-Y. Thibon, Noncommutative symmetric functions, Adv. Math. 112 (1995), 218-348.
12. I. M. Gelfand and A. Spirin, Some analogues of differential operators on quantum spaces and the correspondent multiparametric "quantum" deformation of general linear groups, preprint (1993).
13. I. Gessel, Multipartite P-partitions and inner products of skew Schur functions, in "Combinatorics and algebra", ed. C. Greene, Contem. Math. 34 (1984), 289-301.
14. A. Gyoja, A q-analogue of Young symmetrizer, Osaka Math. J. 23 (1986), 841-852.
15. F. Hivert, Analogues quasi-symétriques et non-commutatifs des fonctions de HallLittlewood, et modules de Demazure d'une algèbre enveloppante quantique dègènèrèe, C.R.A.S. Paris 326 (1998), 1-6.
16. q(gl(N+ 1)), Hecke Algebra and the Yang-Baxter Equation, Lett. Math. Phys. 11 (1986), 247-252.
17. M. Kashiwara, On Crystal Bases of the q-Analogue of Universal Enveloping Algebras, Duke Math. J. 63 (1991), 465-516.
18. M. Kashiwara and T. Nakashima, Crystal graphs for representations of the q-analogue of classical Lie algebras, J. Algebra 165 (1994), 295-345.
19. C. Kassel, Quantum groups, Springer, 1991.
20. D. Krob, B. Leclerc and J.-Y. Thibon, Noncommutative symmetric functions II: Transformations of alphabets, Int. J. Algebra Comput. 7 (1997), 181-264.
21. D. Krob and J.-Y. Thibon, Noncommutative symmetric functions IV: Quantum linear groups and Hecke algebras at q = 0, J. Algebra Comb. G (1997), 339-376.
22. D. E. Knuth, Permutations, matrices and generalized Young tableaux, Pacific J. Math. 34 (1970), 709-727.
23. A. Lascoux, B. Leclerc and J.-Y. Thibon, Hecke algebras at roots of unity and crustal bases of quantum affine algebras, Commun. Math. Phys. 181 (1996), 205-263.
24. n, Lett. Math. Phys. 35 (1995), 359-374.
25. A. Lascoux and M. P. Schützenberger, Le monoïde plaxique, Quad. del. Ric. Sci. 109 (1981), 129-156.
26. A. Lascoux and M. P. Schützenberger, Keys and standard bases, in Invariant Theory and Tableaux, ed. D. Stanton, Springer, New-York, 1990.
27. B. Leclerc and J.-Y. Thibon, The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at q = 0, Electron. J. Combinatorics 3 (11) (1996).
28. P. Littelman, A plactic algebra for semisimple Lie algebras, Adv. Math. 124 (1996), 312-331.
29. C. Malvenuto and C. Reutenauer, Duality between quasi-symmetric functions and Solomon descent algebra, J. Algebra 177 (1995), 967-982.
30. P. N. Norton, 0-Hecke algebras, J. Austral. Math. Soc. (Series A) 27 (1979), 337-357.
31. J.-C. Novelli, On the hypoplactic monoid, Proc. 8th Conf. on Formal Power Series and Algebraic Combinatorics, Vienna, 1997.
32. C. M. Ringel, Hall algebras and quantum groups, Invent. Math. 101 (1990), 583-592.
33. M. Sweedler, Hopf algebras, W. A. Bejamin Inc., New York, 1969.
34. M. Takeuchi, A two-parameter quantization of GL(n), Proc. Japan Acad. Scr. A 66 (1990), 112-114.
35. J.-Y. Thibon and B.-C.-V. Ung, Quantum quasi-symmetric functions and Hecke algebras, J. Phys. A: Math. Gen. 29 (1996), 7337-7348.