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

Reçu le :
Accepté le :
Publié le :
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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Existence of elementwise invariant vectors in representations of symmetric groups},
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     year = {2024},
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P., Amrutha; Prasad, Amritanshu; S., Velmurugan. Existence of elementwise invariant vectors in representations of symmetric groups. Algebraic Combinatorics, Tome 7 (2024) no. 4, pp. 915-929. doi: 10.5802/alco.369

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