Let m, n ∈ N, V be a 2m-dimensional complex vector space. The irreducible representations of the Brauer's centralizer algebra B_n(-2m) appearing in V~(direct X n) are in 1–1 correspondence to the set of pairs (f,λ), where f ∈ Z with 0 ≤ f ≤ [n/2], and λ |- n-2f satisfying λ_1 ≤ m. In this paper, we first show that each of these representations has a basis consists of eigenvectors for the subalgebra of B_n(-2m) generated by all the Jucys-Murphy operators, and we determine the corresponding eigenvalues. Then we identify these representations with the irreducible representations constructed from a cellular basis of B_n(-2m). Finally, an explicit description of the action of each generator of B_n(-2m) on such a basis is also given, which generalizes earlier work of [15] for Brauer's centralizer algebra B_n(m).
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