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Search: MSC category 20C30 ( Representations of finite symmetric groups )

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1. CJM 2014 (vol 67 pp. 1024)

Ashraf, Samia; Azam, Haniya; Berceanu, Barbu
Representation Stability of Power Sets and Square Free Polynomials
The symmetric group $\mathcal{S}_n$ acts on the power set $\mathcal{P}(n)$ and also on the set of square free polynomials in $n$ variables. These two related representations are analyzed from the stability point of view. An application is given for the action of the symmetric group on the cohomology of the pure braid group.

Keywords:symmetric group modules, square free polynomials, representation stability, Arnold algebra
Categories:20C30, 13A50, 20F36, 55R80

2. CJM 2004 (vol 56 pp. 871)

Schocker, Manfred
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

3. CJM 1997 (vol 49 pp. 133)

Reeder, Mark
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

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