Hyperoctahedral Schur algebras (Q1359035)

This paper gives a description of the centralizing algebra for the natural action of the Weyl group of type \(B_r\) on the \(r\)-th tensor power of a \(2n\)-dimensional space \(V\). That is a description of the endomorphisms of \(V^{\otimes r}\) that commute with the action of \(B_r\). The multiplicative structure of the centralizing algebra is given. Then a similar study is completed for the associated Hecke algebra of type \(B\) acting on such modules.