# Specht modules for quiver Hecke algebras of type $C$

## TL;DR

This paper constructs Specht modules for cyclotomic quiver Hecke algebras of type C, providing explicit bases and character formulas in infinite type, and proposing conjectures for affine type.

## Contribution

It introduces Specht modules for type C quiver Hecke algebras, detailing their bases, properties, and character formulas, and extends the theory to affine type with conjectures.

## Key findings

- Homogeneous bases for Specht modules in type C∞
- Graded character formulas for these modules
- Properties under exact functors $E_i^Λ$ and $F_i^Λ$

## 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.