Abstract
In this short note, we prove that the Gibbs cone of generalized temperatures associated to a minimal coadjoint orbit of a simple Lie group G of Kähler type is not empty. We study the Fisher-Rao metric in the particular case of \(G = \textrm{SL}_2 (\mathbb {R})\). We prove that, in this case, the Gibbs cone equipped with the Fisher-Rao metric is a Riemannian symmetric space.
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Bieliavsky, P., Dendoncker, V., Neuttiens, G., de Maujouy, J.P. (2023). Riemannian Geometry of Gibbs Cones Associated to Nilpotent Orbits of Simple Lie Groups. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14072. Springer, Cham. https://doi.org/10.1007/978-3-031-38299-4_16
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DOI: https://doi.org/10.1007/978-3-031-38299-4_16
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