Bases for local Weyl modules in type $C$

TL;DR

This paper constructs a Poincare-Birkhoff-Witt basis for local Weyl modules of the current algebra of type C, leading to a fermionic character formula that advances understanding of their structure.

Contribution

It provides the first explicit PBW basis for local Weyl modules in type C and derives a fermionic character formula, offering new tools for their analysis.

Findings

Explicit PBW basis for local Weyl modules in type C

Fermionic character formula derived for these modules

Enhanced understanding of module structure in type C

Abstract

We give a Poincare-Birkhoff-Witt type basis for local Weyl modules of the current algebra of type $C$. As a consequence, we get a fermionic character formula for these modules.