Cyclic Characters of Symmetric Groups
Armin Jöllenbeck
and Manfred Schocker
DOI: 10.1023/A:1026592027019
Abstract
We consider characters of finite symmetric groups induced from linear characters of cyclic subgroups. A new approach to Stembridge's result on their decomposition into irreducible components is presented. In the special case of a subgroup generated by a cycle of longest possible length, this amounts to a short proof of the Kra 
kiewicz-Weyman theorem.
kiewicz-Weyman theorem.Pages: 155–161
Keywords: symmetric group; Young tableau; multi major index; induced character; Lie idempotent
Full Text: PDF
References
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2. A.M. Garsia, Combinatorics of the Free Lie Algebra and the Symmetric Group, Academic Press, New York, 1990, pp. 309-382.
3. L. Geissinger, “Hopf algebras of symmetric functions and class functions,” in Comb. Represent. Groupe Symetr., Actes Table Ronde C.N.R.S. Strasbourg
1976. Lecture Notes of Mathematics, Vol. 579, pp. 168-181, 1977.
4. A. J\ddot ollenbeck, “Nichtkommutative Charaktertheorie der symmetrischen Gruppen,” Bayseuther Mathematische Schriften 56 (1999), 1-4.
5. A.A. Klyachko, “Lie elements in the tensor algebra,” Siberian Mathematical Journal 15 (1974), 914-929.
6. W. Kraśkiewiz and J. Weyman, “Algebra of invariants and the action of a Coxeter element,” Preprint, Math. Inst. Univ. Copernic, Torún, Poland, 1987.
7. B. Leclerc, T. Scharf, and J.-Y. Thibon, “Noncummutative cyclic characters of symmetric groups,” Journal of Combinatorial Theory, Series A 75(1) (1996), 55-69.
8. C. Reutenauer, Free Lie Algebras, Oxford University Press, Oxford,
1993. London Mathematical Society Monographs, New Series, Vol. 7.
9. L. Solomon, “A Mackey formula in the group ring of a Coxeter group,” Journal of Algebra 41 (1976), 255-268.
10. W. Specht, “Die linearen Beziehungen zwischen h\ddot oheren Kommutatoren,” Mathematische Zeitschrift 51 (1948), 367-376.
11. J.R. Stembridge, “On the eigenvalues of representations of reflection groups and wreath products,” Pacific Journal of Mathematics 140(2) (1989), 353-396.
12. F. Wever, “Uber Invarianten in Lieschen Ringen,” Mathematische Annalen 120 (1949), 563-580.