Finite convergent presentation of plactic monoid for type C

TL;DR

This paper provides a finite, convergent presentation for the type C plactic monoid using admissible column generators, leveraging symplectic tableaux properties to establish homological finiteness.

Contribution

It introduces a new explicit finite convergent presentation for the type C plactic monoid based on admissible columns.

Findings

The presentation is finite and convergent.

Type C plactic monoids satisfy homological finiteness properties.

The approach uses combinatorial properties of symplectic tableaux.

Abstract

We give an explicit presentation for the plactic monoid for type C using admissible column generators. Thanks to the combinatorial properties of symplectic tableaux, we prove that this presentation is finite and convergent. We obtain as a corollary that plactic monoids for type C satisfy homological finiteness properties.