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The degenerate affine Hecke algebra (dAHA) of any Coxeter group was defined by Drinfeld and Lusztig([Dri],[Lus]). It is generated by the group algebra of the Coxeter group and by the commuting generators yi with some relations. The degenerate double affine Hecke algebra (dDAHA) of a root system was introduced by Cherednik (see [Ch]). It is generated by the the group algebra of the Weyl group, commuting generators yi, and by another kind of commuting generators Xi with some relations. The dAHA corresponding to the Weyl group can be realized as a subalgebra of dDAHA, generated by the Weyl group and the elements yi. The paper [AS] gives a Lie-theoretic construction of representations of the dAHA of type An−1. Namely (see [CEE], section 9), for every slN -bimodule M , an action of the dAHA H of type An−1 is constructed on the space

A Lie-theoretic construction of some representations of the degenerate affine and double affine Hecke algebras of type 𝐵𝐶_{𝑛}