Noncommutative cyclic characters of symmetric groups

Journal of Combinatorial Theory. Series A

Volumn 75, Issue 1, 1996, Pages 55-69

  Leclerc, Bernard ^a   Scharf, Thomas ^b   Thibon, Jean Yves ^c  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITY OF BAYREUTH   (Germany)

^c Ecole Superieure d'Informatique et Genie des Telecommunications   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030186578     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcta.1996.0063     Document Type: Article

References (19)

1. 1. D. BLESSENOHL AND H. LAUE, On Witt's dimension formula and a theorem of Klyachko, Bull. Austral. Math. Soc. 40 (1989), 49-57.
2. 2. G. DUCHAMP, D. KROB, B. LECLERC, AND J.-Y. THIBON, Déformations de projecteurs de Lie, C.R. Acad. Sci. Paris 319 (1994), 909-914.
3. 3. H. O. FOULKES, Characters of symmetric groups induced by characters of cyclic sub-groups, in Combinatorics in "Proceedings Conf. Combin. Math. Inst. Oxford, 1972, Inst. Math. Appl., Southend-on-Sea, 1972," pp. 141-154.
4. 4. I. M. GELFAND, D. KROB, A. LASCOUX, B. LECLERC, V. S. RETAKH, AND J.-Y. THIBON, Noncommutative symmetric functions, Adv. in Math. 112 (1995), 218-348.
5. 5. I. M. GELFAND AND V. S. RETAKH, Determinants of matrices over noncommutative rings, Funct. Anal. Appl. 25 (1991), 91-102.
6. 6. I. M. GELFAND AND V. S. RETAKH, A theory of noncommutative determinants and characteristic functions of graphs, Funct. Anal. Appl. 26 (1992), 1-20; Publ. Lacim, UQAM, Montreal, Vol. 14, pp. 1-26.
7. 6. I. M. GELFAND AND V. S. RETAKH, A theory of noncommutative determinants and characteristic functions of graphs, Funct. Anal. Appl. 26 (1992), 1-20; Publ. Lacim, UQAM, Montreal, Vol. 14, pp. 1-26.
8. 7. I. GESSEL, Multipartite P-partitions and inner product of skew Schur functions, Contemp. Math. 34 (1984), 289-301.
9. 8. A. A. KLYACHKO, Lie elements in the tensor algebra, Siberian Math. J. 15 (1974), 1296-1304.
10. 9. W. KRASKIEWICZ AND J. WEYMAN, Algebra of invariants and the action of a Coxeter element, preprint, Math. Inst. Univ. Copernic, Toruń, Poland.
11. 10. A. LASCOUX, B. LECLERC, AND J.-Y. THIBON, Green polynomials and Hall-Littlewood functions at roots of unity, European J. Combin. 15 (1994), 173-180.
12. 11. I. G. MACDONALD, "Symmetric Functions and Hall Polynomials," Oxford Math. Monographs, Oxford Univ. Press, Oxford, 1979.
13. 12. P. A. MACMAHON, "Combinatory Analysis," Cambridge Univ. Press, Cambridge 1915, 1916; Chelsea, New York, 1960.
14. 13. B. MIELNIK AND J. PLEBAŃSKI, Combinatorial approach to Baker-Campbell-Hausdorff exponents, Ann. Inst. H. Poincaré Sect. A 12 (1970), 215-254.
15. 14. C. REUTENAUER, "Free Lie Algebras," Oxford Univ. Press, Oxford, 1993.
16. 15. T. SCHARF AND J.-Y. THIBON, A Hopf algebra approach to inner plethysm, Adv. in Math. 104 (1994), 30-58.
17. 16. L. SOLOMON, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41 (1976), 255-268.
18. 17. J. R. STEMBRIDGE, On the eigenvalues of representations of reflection groups and wreath products, Pacific J. Math 140 (1989), 353-396.
19. 18. B. C. V. UNG, "NCSF, a MAPLE Package for Noncommutative Symmetric Functions," Preprint, Université de Marne-la-vallée, 1994.