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Noncommutative Cyclic Characters of Symmetric Groups

✍ Scribed by Bernard Leclerc; Thomas Scharf; Jean-Yves Thibon

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 485 KB
Volume: 75
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0063

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✦ Synopsis

We define noncommutative analogues of the characters of the symmetric group which are induced by transitive cyclic subgroups (cyclic characters). We investigate their properties by means of the formalism of noncommutative symmetric functions. The main result is a multiplication formula whose commutative projection gives a combinatorial formula for the resolution of the Kronecker product of two cyclic representations of the symmetric group. This formula can be interpreted as a multiplicative property of the major index of permutations.

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