Conversations with Flaschka: Kac-Moody groups and Verblunsky coefficients

TL;DR

This paper explores the application of the Toda lattice to complex Lie groups related to indefinite Kac-Moody algebras and introduces a new example of the Verblunsky correspondence, stemming from discussions with Hermann Flaschka.

Contribution

It presents novel connections between Toda lattice dynamics and indefinite Kac-Moody Lie groups, and provides a new example in the Verblunsky correspondence.

Findings

Link between Toda lattice and indefinite Kac-Moody groups

New example of Verblunsky correspondence

Insights into complex Lie group structures

Abstract

In this paper we discuss two items which in one way or another originated from conversations with Hermann Flaschka and his students. The first is an application of the Toda lattice to the question of whether there exists a complex Lie group (with certain properties) associated to an indefinite type Kac-Moody Lie algebra. The second concerns a new example of the Verblunsky correspondence.