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Specht modules for quiver Hecke algebras of type $C$ (1703.06425v2)
Published 19 Mar 2017 in math.RT and math.CO
Abstract: We construct and investigate Specht modules $\mathcal{S}\lambda$ for cyclotomic quiver Hecke algebras in type $C{(1)}_\ell$ and $C_\infty$, which are labelled by multipartitions $\lambda$. It is shown that in type $C_\infty$, the Specht module $\mathcal{S}\lambda$ 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 $C{(1)}_\ell$, we propose a conjecture.