  We define a new class of algebras, cyclotomic Temperley-Lieb algebras of type
D, in a diagrammatic way, which is a generalization of Temperley-Lieb algebras
of type D. We prove that the cyclotomic Temperley-Lieb algebras of type D are
cellular. In fact, an explicit cellular basis is given by means of
combinatorial methods. After determining all the irreducible representations of
these algebras, we give a necessary and sufficient condition for a cyclotomic
Temperley-Lieb algebra of type D to be quasi-hereditary.
