×
Schocker, Manfred

Multiplicities of higher Lie characters. (English) Zbl 1037.20013

J. Aust. Math. Soc. 75, No. 1, 9-21 (2003).
Author’s summary: The higher Lie characters of the symmetric group \(S_n\) arise from the Poincaré-Birkhoff-Witt basis of the free associative algebra. They are indexed by partitions of \(n\) and sum up to the regular character of \(S_n\). A combinatorial description of the multiplicities of their irreducible constituents is given. As a special case the Kraśkiewicz-Weyman result on the multiplicities of the classical Lie character is obtained.
Reviewer: Yakov Berkovich (Afula)

Cited in 2 Reviews
Cited in 8 Documents

MSC:

20C30 Representations of finite symmetric groups
05E10 Combinatorial aspects of representation theory
17B01 Identities, free Lie (super)algebras

Keywords:

free Lie algebras; tensor algebras; composition multiplicities; partitions; symmetric groups
Cite Review PDF
Full Text: DOI

References:

[1] Hardy, An introduction to the theory of numbers (1960) · Zbl 0086.25803
[2] DOI: 10.1006/jabr.1999.7887 · Zbl 0956.16017 · doi:10.1006/jabr.1999.7887
[3] DOI: 10.1006/jabr.1996.0090 · Zbl 0864.20007 · doi:10.1006/jabr.1996.0090
[4] Bergeron, Invariant theory and tableaux (Minneapolis, MN, 1988) pp 166– (1990)
[5] Witt, J. Reine Angew. Math. 177 pp 152– (1937)
[6] DOI: 10.2307/2371691 · Zbl 0061.04201 · doi:10.2307/2371691
[7] DOI: 10.1016/0021-8693(76)90182-4 · Zbl 0355.20007 · doi:10.1016/0021-8693(76)90182-4
[8] Reutenauer, Free Lie algebras (1993) · Zbl 0798.17001
[9] Kraśkiewicz, Bayr. Math. Schr. 63 pp 265– (2001)
[10] DOI: 10.1006/jcta.1996.0063 · Zbl 0857.20005 · doi:10.1006/jcta.1996.0063
[11] DOI: 10.1007/BF00966559 · Zbl 0325.15018 · doi:10.1007/BF00966559
[12] DOI: 10.1023/A:1026592027019 · Zbl 0979.20017 · doi:10.1023/A:1026592027019
[13] Jöllenbeck, Bayr. Math. Schr. 56 pp 1– (1999)
[14] James, The representation theory of the symmetric group (1981)
[15] DOI: 10.1016/0001-8708(89)90020-0 · Zbl 0716.20006 · doi:10.1016/0001-8708(89)90020-0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.