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no. 4
Existence of elementwise invariant vectors in representations of symmetric groups
P., Amrutha1; Prasad, Amritanshu2, 3; S., Velmurugan2, 3
1 Chennai Mathematical Institute H1, SIPCOT IT Park Siruseri Kelambakkam 603103, India
2 The Institute of Mathematical Sciences CIT Campus, Taramani Chennai 600113, India
3 Homi Bhabha National Institute Anushakti Nagar, Mumbai 400094, India
Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 915-929.

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. We find that a majority of pairs (λ,μ) have this property, with only a few simple exceptions.

Received:
Accepted:
Published online:
DOI: 10.5802/alco.369
Classification: 20C30, 05E10
Keywords: locally invariant vectors, symmetric groups, representations

P., Amrutha 1; Prasad, Amritanshu 2, 3; S., Velmurugan 2, 3

1 Chennai Mathematical Institute H1, SIPCOT IT Park Siruseri Kelambakkam 603103, India
2 The Institute of Mathematical Sciences CIT Campus, Taramani Chennai 600113, India
3 Homi Bhabha National Institute Anushakti Nagar, Mumbai 400094, India
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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P., Amrutha; Prasad, Amritanshu; S., Velmurugan. Existence of elementwise invariant vectors in representations of symmetric groups. Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 915-929. doi : 10.5802/alco.369. https://alco.centre-mersenne.org/articles/10.5802/alco.369/

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