For each of the five faithful transitive permutation representations of the order-96 complex reflection group H1, the centralizer ring of every tensor power is described as a direct sum of matrix algebras.
Centralizer Algebras of Two Permutation Groups of Order 1344
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There are two permutation groups that they share the same character table of order 1344. We take up natural representations on 8 and 14 letters respectively. The purpose of this paper is to examine the semi-simple structure of centralizing algebras in the tensor representation.
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Some calculations of centralizer rings of a complex reflection group
For each of the five faithful transitive permutation representations of the order-96 complex reflection group H1, the centralizer ring of every tensor power is described as a direct sum of matrix algebras.