Specht modules for quiver Hecke algebras of type $C$

Abstract

We construct and investigate Specht modules ${\mathcal{S}}^{\lambda }$ for cyclotomic quiver Hecke algebras in type $C_{\ell }^{(1)}$ 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 $C_{\ell }^{(1)}$, we propose a conjecture.

57 pages, minor revision, to appear in Publications of the Research Institute for Mathematical Sciences

References in corpus (4)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• On the semisimplicity of the cyclotomic quiver Hecke algebra of type C

Cited by in corpus (6)

• Graded dimensions and monomial bases for the cyclotomic quiver Hecke algebras
• Cellularity and subdivision of KLR and weighted KLRW algebras
• Content systems and deformations of cyclotomic KLR algebras of type $A$ and $C$
• Morita equivalences between cyclotomic KLR algebras in types ${\mathtt{C}}_{\infty }$ and ${\mathtt{A}}_{\infty }$
• Representation type of higher level cyclotomic quiver Hecke algebras in affine type C
• A remark on convolution products for quiver Hecke algebras