Specht Modules for Quiver Hecke Algebras of Type C

We construct and investigate Specht modules Sλ for cyclotomic quiver Hecke algebras of types C⁽¹⁾_ and C_∞ , which are labelled by multipartitions λ . It is shown that in type C_∞ , the Specht module Sλ has a homogeneous basis indexed by standard tableaux of shape λ , which yields a graded character formula and good properties with the exact functors E_i^Λ and F_i^Λ . For type C⁽¹⁾_ , we propose a conjecture.