Noncommutative symmetric functions VI: Free quasi-symmetric functions and related algebras

International Journal of Algebra and Computation

Volumn 12, Issue 5, 2002, Pages 671-717

  Duchamp, Gérard ^a   Hivert, Florent ^b   Thibon, Jean Yves ^b  

^a UNIVERSITÉ DE ROUEN   (France)

^b Université de Marne la Vallée   (France)

Author keywords

Hecke algebras; Poset; Quasi symmetric functions; Symmetric functions

Indexed keywords

EID: 0036814466     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196702001139     Document Type: Article

References (32)

1. L. Abrams, Modules, comodules and cotensor products over Frobenius algebras, math.RA/9806044.
2. M. Auslander, I. Reiten and S.-O. Smalø, Representation theory of Artin algebras, Cambridge Stud. Adv. Math., Cambridge University Press, 36 (1997).
3. n, C. R. Acad. Sci. Paris, Ser. A 275 (1972), 569-572.
4. C.W. Curtis and I. Reiner, Methods of Representation Theory, 2 Vols., Wiley-Interscience, New York, 1981.
5. G. Duchamp, Orthogonal projection onto the free Lie algebra, Theoret. Comput. Sci. 79 (1991), 227-239.
6. G. Duchamp, A. Klyachko, D. Krob and J.-Y. Thibon, Noncommutative symmetric functions III: Deformations of Cauchy and convolution algebras, Discrete Math. Theoret. Comput. Sci. 1 (1997), 159-216.
7. G. Duchamp, F. Hivert and J.-Y. Thibon, Une gnralisation des fonctions quasi-symtriques et des fonctions symtriques non commutatives, C. R. Acad. Sci. Paris, Sér. I Math. 328(12) (1999), 1113-1116.
8. G. Duchamp, F. Hivert and J.-Y. Thibon, Some generalizations of quasi-symmetric functions and noncommutative symmetric functions, Formal Power Series and Algebraic Combinatorics Moscow, 2000, Springer, Berlin, 2000, pp. 170-178.
9. G. Duchamp, D. Krob, B. Leclerc and 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.
10. D. Foata and M.P. Schützenberger, Major index and inversion number of permutations, Math. Nachr. 83 (1978), 143-159.
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. Gessel, Multipartite P-partitions and inner products of skew Schur functions, in Combinatorics and algebra, ed. C. Greene, Contemp. Math. 34 (1984), 289-301.
13. E.L. Green and R. Martínez-Villa, Koszul and Yoneda algebras, in Representation Theory of Algebras, CMS Conf. Proc. 18 (1996), 247-297.
14. E.L. Green and R. Martínez-Villa, Koszul and Yoneda algebras II, in Algebras and Modules II, CMS Conf. Proc. 24 (1998), 227-244.
15. V.G. Kac, Some remarks on representations of quivers and infinite root systems, Representation Theory, II, Proc. Second Int. Conf., Carleton University, Ottawa, Ontario, 1979, pp. 311-327, Lecture Notes in Mathematics 832, Springer, Berlin, 1980.
16. A.A. Klyachko, private communication (1995).
17. D. Krob, B. Leclerc and J.-Y. Thibon, Noncommutative symmetric functions II: Transformations of alphabets, Int. J. Alg. Comput. 7 (1997), 181-264.
18. D. Krob and J.-Y. Thibon, Noncommutative symmetric functions IV: Quantum linear groups and Hecke algebras at q = 0, J. Algebra. Combin. 6 (1997), 339-376.
19. A. Lascoux, Anneau de Grothendieck de la variété de drapeaux, in The Grothendieck Festschrift, Vol. III, Progr. Math. 88 (1990), 1-34.
20. A. Lascoux, B. Leclerc and J.-Y. Thibon, The plactic monoid, Algebraic Combinatorics on Words, ed. M. Lothaire, chap. 5, Cambridge University Press, 2002.
21. J.-L. Loday and M. Ronco, Hopf algebra of the planar binary trees, Adv. Math. 139 (1998), 293-309.
22. C. Malvenuto, P-partitions and the plactic congruence, Graphs Combin. 9 (1993), 63-73.
23. C. Malvenuto and C. Reutenauer, Duality between quasi-symmetric functions and Solomon descent algebra, J. Algebra 177 (1995), 967-982.
24. R. Martínez-Villa, Applications of Koszul algebras: The preprojective algebra, in Representation Theory of Algebras, CMS Conf. Proc. 18 (1996), 487-504.
25. P.N. Norton, 0-Hecke algebras, J. Austral. Math. Soc. Ser. A 227 (1979), 337-357.
26. J.-C. Novelli, On the hypoplactic monoid, Proc. 8th Conf. Formal Power Series Algebraic Combin., Vienna, 1997.
27. S. Poirier and C. Reutenauer, Algèbre de Hopf des tableaux, Ann. Sci. Math., Quebec 19 (1995), 79-90.
28. C. Reutenauer, Free Lie Algebras, Oxford Science Publications (1993).
29. R.P. Stanley, Ordered structures and partitions, Mem. Amer. Math. Soc. 119 (1972).
30. R.P. Stanley, Generalized riffle shuffles and quasisymmetric functions, preprint, 1999.
31. J.-Y. Thibon and B.-C.-V. Ung, Quantum quasi-symmetric functions and Hecke algebras, J. Phys. A: Math. Gen. 29 (1996), 7337-7348.
32. B.-C.-V. Ung, Combinatorial identities for series of quasi-symmetric functions, Uni-versité de Marne-la-Vallée, preprint IGM 98-15.