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# Representation Stability of Power Sets and Square Free Polynomials

Published:2014-11-03
Printed: Oct 2015
• 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
 MSC Classifications: 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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