AG Lie-Gruppen: T. Simon (FAU): Gibbs states of Lie groups and characterization of Gibbs elements

Gibbs states of Lie groups and characterization of Gibbs elements

Vortragender: Tobias Simon, FAU

Abstract:

Motivated by the concept of KMS states and more specifically Gibbs states in
Quantum Statistical Mechanics, we study Lie algebraic and representation
theoretic aspects of Gibbs states of Lie groups. These correspond to an
irreducblie unitary representation \rho and an generator X in the Lie algebra
satisfying \tr(e^{i\del\pi(X)})<\infty. This property is well known for unitary
highest weight representations of admissible Lie groups and elements of a
certain cone in the Lie algebra. We show, that this is not only a sufficient but
also necessary condition for the Lie algebra, the representation and the generator.