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A generating set of Solomon's descent algebra

✍ Scribed by Manfred Schocker

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
90 KB
Volume
263
Category
Article
ISSN
0021-8693

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✦ Synopsis

Solomon's descent algebra is generated by sums of descent classes corresponding to certain hook shapes. This particularly implies that the ring of class functions of any finite symmetric group S n is generated by the irreducible characters corresponding to certain hook partitions of n. As another consequence, a second generating set of Solomon's descent algebra (and of the ring of class functions of S n ) is obtained related to the major index of permutations.

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In a previous paper (see A. Garsia and C. Reutenauer (Adt,. in Math. 77, 1989, 189-262)). we have studied algebraic properties of the descent algebras X,,, and shown how these are related to the canonical decomposition of the free Lie algebra corresponding to a version of the PoincarE-Birkhoff-Witt