Abstract view
Lie Elements and Knuth Relations


Published:20040801
Printed: Aug 2004
Abstract
A coplactic class in the symmetric group $\Sym_n$ consists of all
permutations in $\Sym_n$ with a given Schensted $Q$symbol, and may
be described in terms of local relations introduced by Knuth. Any
Lie element in the group algebra of $\Sym_n$ which is constant on
coplactic classes is already constant on descent classes. As a
consequence, the intersection of the Lie convolution algebra
introduced by Patras and Reutenauer and the coplactic algebra
introduced by Poirier and Reutenauer is the direct sum of all
Solomon descent algebras.
MSC Classifications: 
17B01, 05E10, 20C30, 16W30 show english descriptions
Identities, free Lie (super)algebras Combinatorial aspects of representation theory [See also 20C30] Representations of finite symmetric groups Coalgebras, bialgebras, Hopf algebras (See also 16S40, 57T05); rings, modules, etc. on which these act
17B01  Identities, free Lie (super)algebras 05E10  Combinatorial aspects of representation theory [See also 20C30] 20C30  Representations of finite symmetric groups 16W30  Coalgebras, bialgebras, Hopf algebras (See also 16S40, 57T05); rings, modules, etc. on which these act
