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Representation stability of power sets and square free polynomials

  • Samia Ashraf,
    Abdus Salam School of Mathematical Sciences, GC University, Lahore-Pakistan
  • Haniya Azam,
    Abdus Salam School of Mathematical Sciences, GC University, Lahore-Pakistan
  • Barbu Berceanu,
    Abdus Salam School of Mathematical Sciences, GC University, Lahore-Pakistan
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Abstract

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 symmetric group modules, square free polynomials, representation stability, Arnold algebra
MSC Classifications: 20C30, 13A50, 20F36, 55R80 show english descriptions Representations of finite symmetric groups
Actions of groups on commutative rings; invariant theory [See also 14L24]
Braid groups; Artin groups
Discriminantal varieties, configuration spaces
20C30 - Representations of finite symmetric groups
13A50 - Actions of groups on commutative rings; invariant theory [See also 14L24]
20F36 - Braid groups; Artin groups
55R80 - Discriminantal varieties, configuration spaces
 

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