## Abstract

We compute the weights, i.e. the values at the minimal idempotents, for the Markov trace on the Hecke algebra of type *B _{n}* and type

*D*. In order to prove the weight formula, we define representations of the Hecke algebra of type

_{n}*B*onto a reduced Hecke algebra of type

*A*. To compute the weights for type

*D*we use the inclusion of the Hecke algebra of type

*D*into the Hecke algebra of type

*B*.

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