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Let W(Bn) be the Weyl group of type Bn and H(Bn) be the associated Iwahori–Hecke algebra. In this paper, we study the n-tensor space V⊗n (where dimV=2m) with natural actions (introduced in [R.M. Green, Hyperoctahedral Schur algebras, J. Algebra 192 (1997) 418–438]) of W(Bn) and of H(Bn). For each composition λ=(λ1,…,λm) of n, let eλ be the corresponding initial basis element of V⊗n (see (3.8) for...
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