A Morita equivalence theorem for Hecke algebra \({\mathcal H}_q(D_n)\) when \(n\) is even (Q1849394)

\textit{R. Dipper} and \textit{G. James} [J. Algebra 146, No. 2, 454-481 (1992; Zbl 0808.20016)] proved a Morita equivalence theorem for Hecke algebras of type \(B_n\) given certain restrictions. Under similar restrictions, a Morita equivalence theorem for \(H_q(D_n)\), the Hecke algebra of type \(D_n\) was proved in the case where \(n\) is odd by \textit{C. Pallikaros} [J. Algebra 169, No. 1, 20-48 (1994; Zbl 0833.20019)] and in the article under review this result is generalized to the case where \(n\) is even. As a consequence all the irreducible \(H_q(D_n)\)-modules are constructed under the restriction that a certain polynomial in \(q\) is non-zero.