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Locally invariant vectors in symmetric group

  • Mr. Velmurugan, Research Scholar, The Institute of Mathematical Sciences, Chennai

We determine when a permutation with cycle type \(μ\) admits a non-zero invariant vector in the irreducible representation \(V_λ\) of the symmetric group. Most pairs \((λ,μ)\) have this property, with only a few simple exceptions. This is a joint work with Amrutha P and Amritanshu Prasad.