Conjugacy classes in discrete Heisenberg groups

TL;DR

This paper investigates conjugacy classes in extended discrete Heisenberg groups, identifying invariants and providing explicit descriptions in specific cases like the integer Heisenberg group.

Contribution

It introduces new invariants for conjugacy classes in extended discrete Heisenberg groups and makes these invariants explicit in certain cases.

Findings

Identified invariants of conjugacy classes in extended discrete Heisenberg groups.

Explicit descriptions of invariants for the integer Heisenberg group.

Enhanced understanding of conjugacy class structure in these groups.

Abstract

We study some extension of a discrete Heisenberg group coming from the theory of loop-groups and find invariants of conjugacy classes in this group. In some cases including the case of the integer Heisenberg group we make these invariants more explicit.