The Kazhdan–Lusztig Basis and the Temperley–Lieb Quotient in Type D

Let be a Hecke algebra associated with a Coxeter system of type D, and let be the corresponding Temperley–Lieb quotient. The algebra admits a canonical basis, which facilitates the construction of irreducible representations. In this paper, we explain the relationship between the canonical basis of and the Kazhdan–Lusztig basis of