Induced Discrete Series Representations for Hecke Algebras of Types $B_{n}^{\mathrm{aff}}$ and $C_{n}^{\mathrm{aff}}$

Recently, Delorme and Opdam [7] have generalized the theory of R-groups towards affine Hecke algebras with unequal labels. We apply their results in the case where the affine Hecke algebra is of type $C_{n}^{\mathrm{aff}}$ or $B_{n}^{\mathrm{aff}}$, and the induced discrete series representation has positive central character. We show that the R-group of such an induced representation is isomorphic to $(\mathbb{Z}/2\mathbb{Z})^{d}$, and that the representation decomposes multiplicity-free into $2^{d}$ irreducible summands. The number d is calculated by combinatorial means.