Representation theory of the higher-order peak algebras
Jean-Christophe Novelli
, Franco Saliola
and Jean-Yves Thibon
DOI: 10.1007/s10801-010-0223-y
Abstract
The representation theory (idempotents, quivers, Cartan invariants, and Loewy series) of the higher-order unital peak algebras is investigated. On the way, we obtain new interpretations and generating functions for the idempotents of descent algebras introduced in Saliola (J. Algebra 320:3866, 2008).
Pages: 465–495
Keywords: keywords noncommutative symmetric functions; peak algebras; finite dimensional algebras; descent algebras
Full Text: PDF
References
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2. Aguiar, M., Nyman, K., Orellana, R.: New results on the peak algebra. J. Algebraic Comb. 23(2), 149-188 (2006)
3. Aguiar, M., Novelli, J.-C., Thibon, J.-Y.: Unital versions of the higher order peak algebras.
4. Benson, D.J.: Representations and Cohomology. I: Basic Representation Theory of Finite Groups and Associative Algebras, 2nd edn. Cambridge Studies in Advanced Mathematics, vol.
30. Cambridge University Press, Cambridge (1998)
5. Bergeron, N.: A decomposition of the descent algebra of the hyperoctahedral group, II. J. Algebra 148, 98-122 (1992)
6. Bergeron, F., Bergeron, N.: Orthogonal idempotents in the descent algebra of Bn and applications. J. Pure Appl. Algebra 79, 109-129 (1992)
7. Bergeron, N., Hivert, F., Thibon, J.-Y.: The peak algebra and the Hecke-Clifford algebras at q =
0. J. Comb. Theory A 117, 1-19 (2004)
8. Blessenohl, D., Laue, H.: The module structure of Solomon's descent algebra. J. Aust. Math. Soc. 72(3), 317-333 (2002)
9. Chow, C.-O.: Noncommutative symmetric functions of type B. Ph.D. Thesis, MIT, 2001
10. Garsia, A.M., Reutenauer, C.: A decomposition of Solomon's descent algebra. Adv. Math. 77, 189- 262 (1989)
11. Gelfand, I.M., Krob, D., Lascoux, A., Leclerc, B., Retakh, V.S., Thibon, J.-Y.: Noncommutative symmetric functions. Adv. Math. 112, 218-348 (1995)
12. Hivert, F., Thiéry, N.: MuPAD-Combinat, an open-source package for research in algebraic combina- torics. Sémin. Lothar. Comb. 51, 70 (2004) (electronic)
13. Krob, D., Thibon, J.-Y.: Higher order peak algebras. Ann. Comb. 9, 411-430 (2005)
14. Krob, D., Leclerc, B., Thibon, J.-Y.: Noncommutative symmetric functions II: Transformations of alphabets. Int. J. Algebra Comput. 7, 181-264 (1997)
15. Mantaci, R., Reutenauer, C.: A generalization of Solomon's descent algebra for hyperoctahedral groups and wreath products. Commun. Algebra 23, 27-56 (1995)
16. Novelli, J.-C., Thibon, J.-Y.: Superization and (q, t)-specialization in combinatorial Hopf algebras. [math.CO]
17. Saliola, F.: On the quiver of the descent algebra. J. Algebra 320, 3866-3894 (2008)
18. Stein, W.A., et al.: Sage mathematics software (version 3.3). The Sage Development Team, 2009.
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