A presentation of relative unitary Steinberg groups

TL;DR

This paper provides explicit presentations of certain relative Steinberg groups associated with odd form rings and specific Chevalley group schemes, extending known results for simply laced systems.

Contribution

It introduces explicit presentations for relative odd unitary and doubly laced Steinberg groups over rings, broadening the class of groups with known presentations.

Findings

Explicit presentations for relative odd unitary Steinberg groups.

Explicit presentations for relative doubly laced Steinberg groups.

Extension of known results to new types of root systems.

Abstract

We find an explicit presentation of relative odd unitary Steinberg groups constructed by odd form rings and of relative doubly laced Steinberg groups over commutative rings, i.e. the Steinberg groups associated with the Chevalley group schemes of the types $\mathsf B_\ell$, $\mathsf C_\ell$, $\mathsf F_4$ for $\ell \geq 3$. For simply laced root systems such result is already known.