Conversations with Flaschka: Kac-Moody groups and Verblunsky coefficients. (English) Zbl 1527.37060
Summary: In this paper two items are discussed 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 an exponential map associated to an indefinite type Kac-Moody Lie algebra. The second concerns a new example of the Verblunsky correspondence.
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37J37 | Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| 17B80 | Applications of Lie algebras and superalgebras to integrable systems |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
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