Functional relations for zeta-functions of weight lattices of Lie groups of type $A_3$

TL;DR

This paper investigates zeta-functions associated with weight lattices of certain Lie groups of type A3, deriving functional relations and new evaluation formulas for these functions.

Contribution

It introduces new functional relations and evaluation formulas specifically for zeta-functions of SU(4), SO(6), and PU(4).

Findings

Derived functional relations for zeta-functions of these Lie groups.

Established new classes of evaluation formulas.

Enhanced understanding of zeta-functions in the context of Lie group weight lattices.

Abstract

We study zeta-functions of weight lattices of compact connected semisimple Lie groups of type $A_3$. Actually we consider zeta-functions of SU(4), SO(6) and PU(4), and give some functional relations and new classes of evaluation formulas for them.