Acyclic Complexes Related to Noncommutative Symmetric Functions
F. Bergeron
and D. Krob
DOI: 10.1023/A:1008622519966
Abstract
In this paper, we show how to endow the algebra of noncommutative symmetric functions with a natural structure of cochain complex which strongly relies on the combinatorics of ribbons, and we prove that the corresponding complexes are acyclic.
Pages: 103–117
Keywords: noncommutative symmetric functions; complexes; ribbons
Full Text: PDF
References
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2. G. Duchamp, A. Klyachko, D. Krob, and J.-Y. Thibon, “Noncommutative symmetric functions III: Deformations of Cauchy and convolution algebras,” LITP Technical Report 96, Paris, 1996.
3. G. Duchamp, D. Krob, B. Leclerc, and J.-Y. Thibon, “Déformations de projecteurs de Lie,” C.R. Acad. Sci. Paris 319 (1994), 909-914.
4. I.M. Gelfand, D. Krob, A. Lascoux, B. Leclerc, V.S. Retakh, and J.-Y. Thibon, “Noncommutative symmetric functions,” Adv. in Math. 112(2) (1995), 218-348.
5. I. Gessel, “Multipartite P-partitions and inner product of skew Schur functions,” Contemporary Mathematics 34 (1984), 289-301.
6. D. Krob, B. Leclerc, and J.-Y. Thibon, “Noncommutative symmetric functions II: Transformations of alphabets,” LITP Technical Report 95-07, Paris, 1995.
7. D. Krob and J.-Y. Thibon, “Noncommutative symmetric functions IV: Quantum linear groups and Hecke algebras at q = 0,” LITP Technical Report 96, Paris, 1996.
8. B. Leclerc, T. Scharf, and J.-Y. Thibon, “Noncommutative cyclic characters of symmetric groups,” preprint, 1995.
9. I.G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford, 1995.
10. C. Malvenuto and C. Reutenauer, “Duality between quasi-symmetric functions and the Solomon descent algebra,” J. Algebra 177 (1995), 967-982.
11. A.I. Molev, “Noncommutative symmetric functions and Laplace operators for classical Lie algebras,” preprint, 1994.
12. C. Reutenauer, Free Lie Algebras, Oxford University Press, 1993.
13. L. Solomon, “A Mackey formula in the group ring of a Coxeter group,” J. Algebra 41 (1976), 255-268.