Double cyclotomic symmetric groups.
This paper considers the structure and representation theory of certain finite dimensional quotients \(H_r\) of the toroidal symmetric groups. The authors prove that \(H_r\) is a cellular algebra by constructing a cellular basis for \(H_r\). Permutation modules and corresponding endomorphism algebras for \(H_r\) are also studied. The main result of this paper is a kind of generalization of the result of Dipper-James-Mathas for Ariki-Koike algebras to the case of cyclotomic toroidal symmetric groups.
scientific article; zbMATH DE number 2174888