Noncommutative and quasi-symmetric analogues of Hall-Littlewood functions, and Demazure modules of a degenerate quantized enveloping algebra;Analogues non-commutatifs et quasi-symétriques des fonctions de Hall-Littlewood, et modules de Demazure d'une algèbre enveloppante quantique dégénérée

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 326, Issue 1, 1998, Pages 1-6

  Hivert, Florent ^a  

^a Université de Marne la Vallée   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031637688     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(97)82703-6     Document Type: Article

References (21)

1. [1] M. Demazure, Une formule des caractères, Bull. Sc. Math., 98 (1974), 163-172.
2. n, Proc. London Math. Soc., 63 (1991), 165-211.
3. [3] G. Duchamp, D. Krob, A. Lascoux, B. Leclerc, T. Scharf, J.-Y. Thibon, Euler-Poincaré characteristic and polynomial representations of Iwahori-Hecke algebras, Publ. RIMS, Kyoto Univ., 31 (1995), 179-201.
4. [4] G. Duchamp, D. Krob, B. Leclerc, J.-Y. Thibon, Fonctions quasi-symétriques, fonctions symétriques non commutatives, et algèbres de Hecke à q = 0, C. R. Acad. Sci. Paris, 322 (1996), 107-112.
5. [5] I.M. Gelfand, D. Krob, B. Leclerc, A. Lascoux, V.-S. Relakh, J.-Y. Thibon, Noncommutative symmetric functions, Adv. Math., 112 (1995), 218-348.
6. [6] I. Gessel, Multipartite P-partitions and inner products of skew Schur functions, in: Combinatorics and algebra, C. Greene Ed., Contemporary Mathematics, 34 (1984), 289-301.
7. [7] J.-A. Green, The characters of the finite general linear groups, Trans. Amer. Math. Soc., 80 (1955), 402-47.
8. [8] R. Hotta, T.-A. Springer, A specialization theorem for certain Weyl group representations and application to the Green polynomials of unitary groups, Inv. Math., 41 (1977), 113-27.
9. [9] A.-N. Kirillov, N.-Y. Reshetikhin, Bethe Ansatz and the combinatorics of Young tableaux. J. Sov. Math., 41 (1988), 925-955.
10. n), in: Proc. 9ème conf. Formal power series and algebraic combinatorics, C. Krattenthaler Ed., Vienne, 1997.
11. [11] D. Krob, J.-Y. Thibon, Noncommutative symmetric functions IV: Quantum linear groups and Hecke algebras at q = 0, J. Alg. Comb., 41 (1996), 339-376.
12. N), Int. J. Alg. and Comp. (1997) (à paraître).
13. [13] A. Lascoux, B. Leclerc, J.-Y. Thibon, Green polynomials and Hall-Littlewood functions at roots of unity, Europ. J. Combinatorics, 15 (1994), 173-180.
14. [14] A. Lascoux, B. Leclerc, J.-Y. Thibon, Ribbon tableaux, Hall-Littlewood functions, quantum affine algebras, and unipotent varieties, J. Math. Phys., 38(2) (1997), 1041-1068.
15. [15] A. Lascoux, M.-P. Schützenberger, Symmetry and flags manifolds, in: Invariant Theory, L.N. Springer, 996 (1983), 118-144.
16. [16] D.-E. Littlewood, On certain symmetric functions, Proc. London Math. Soc., 43 (1961), 485-498.
17. [17] G. Lusztig, Equivariant K-theory and representations of Hecke algebras, Proc. Amer. Math. Soc., 94 (1985), 337-342.
18. [18] I.G. Macdonald, Symmetric functions and Hall polynomials, C Clarendon Press, 1995.
19. [19] I.G. Macdonald, Notes on Schubert Polynomials, Publications du LACIM, UQAM. Montréal, 1991.
20. [20] A. Nakayashiki, Y. Yamada, Kostka polynomials and energy fonctions in solvable lattice models, prépublication, q-alg/9512027.
21. [21] M. Takeuchi, A two-parameter quantization of GL(n), Proc. Japan Acad., 66, Ser. A (1990), 112-114.