Necessary and sufficient conditions for the irreducibility of a linear representation of the braid group $$B_n$$ B n

Autor: Mohamad N. Nasser
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Arabian Journal of Mathematics, Vol 13, Iss 2, Pp 333-339 (2024)
Druh dokumentu: article
ISSN: 2193-5343
2193-5351
DOI: 10.1007/s40065-024-00468-x
Popis: Abstract Valerij G. Bardakov and P. Bellingeri introduced a new linear representation $$\bar{\rho }_F$$ ρ ¯ F of degree $$n+1$$ n + 1 of the braid group $$B_n$$ B n . We study the irreducibility of this representation. We prove that $$\bar{\rho }_F$$ ρ ¯ F is reducible to the degree $$n-1$$ n - 1 . Moreover, we give necessary and sufficient conditions for the irreducibility of the complex specialization of its $$n-1$$ n - 1 degree composition factor $$\bar{\phi }_F$$ ϕ ¯ F .
Databáze: Directory of Open Access Journals
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