1. CJM 2004 (vol 56 pp. 871)
|Lie Elements and Knuth Relations |
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.
Keywords:symmetric group, descent set, coplactic relation, Hopf algebra,, convolution product
Categories:17B01, 05E10, 20C30, 16W30
2. CJM 1997 (vol 49 pp. 133)
|Exterior powers of the adjoint representation |
Exterior powers of the adjoint representation of a complex semisimple Lie algebra are decomposed into irreducible representations, to varying degrees of satisfaction.
Keywords:Lie algebras, adjoint representation, exterior algebra
Categories:20G05, 20C30, 22E10, 22E60