Séminaire Lotharingien de Combinatoire, 91B.66 (2024), 11 pp.
Amrutha P., Amritanshu Prasad and Velmurugan S.
Locally Invariant Vectors in Representations of Symmetric Groups
Abstract.
For each permutation w in Sn and each irreducible representation
(ρλ,Vλ) of
Sn, we determine when ρλ(w)
admits a non-zero invariant vector in Vλ.
We find that non-zero invariant vectors exist in most cases, with very few exceptions.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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