Crystal bases and simple modules for Hecke algebra of type Dn

Let (respectively ) be the Hecke algebra of type Bn (respectively of type Dn) over the complex numbers field . Let ζ be a primitive 2ℓth root of unity in . For any Kleshchev bipartition (with respect to (ζ,1,−1)) λ=(λ(1),λ(2)) of n, let be the corresponding irreducible -module. In the present paper we explicitly determine which split and which remains irreducible when restricts to . This yields a complete classification of all the simple modules for Hecke algebra . Our proof makes use of the crystal bases theory for the Fock representation of the quantum affine algebra and deep result of Arikiʹs proof of LLTʹs conjecture [J. Math. Kyoto Univ. 36 (1996) 789–808].