We prove two relations for the antisymmetrizer in the Hecke algebra and derive certain restrictions imposed by these relations on unitary representations of the Hecke algebra on tensor powers of the space ${\mathbb C}^n$.
On orthogonal projections related to representations of the Hecke algebra on a tensor space
A generic algebra associated to certain Hecke algebras
A new integral basis for the centre of the Hecke algebra of type A
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