Specht Modules for Quiver Hecke Algebras of Type $C$

Abstract

We construct and investigate Specht modules $S^{\lambda }$ for cyclotomic quiver Hecke algebras of types $C_{\ell }^{(1)}$ and $C_{\infty }$, which are labelled by multipartitions $\lambda$. It is shown that in type $C_{\infty }$, the Specht module $S^{\lambda }$ has a homogeneous basis indexed by standard tableaux of shape $\lambda$, which yields a graded character formula and good properties with the exact functors $E_i^{\Lambda }$ and $F_i^{\Lambda }$. For type $C_{\ell }^{(1)}$, we propose a conjecture.