Αγαπητοί Συνάδελφοι, Φοιτητές και Φίλοι,
Θα θέλαμε να σας ενημερώσουμε ότι την Πέμπτη 21 Σεπτεμβρίου στην αίθουσα Μ2, 3ος Όροφος της Σ.Θ.Ε. και ώρα 17:30-18:30, στο πλαίσιο του Σεμιναρίου του Τομέα Γεωμετρίας, θα δώσει ομιλία ο Σπύρος Αφεντουλίδης Αλμπάνης (Bar-Ilan University).
Τίτλος: Dirac cohomology and Θ-correspondence for complex dual pairs
Περίληψη: For the last decades, representation theory of Lie groups and algebras has been a very active research topic with a multitude of ramifications and applications. Since the work, in the 1970’s, of Parthasarathy and Atiyah-Schmid, Dirac operators have become efficient tools to describe and classify the unitary dual of a real Lie group G. On the one hand, any irreducible unitary representation occurring in the regular representation L^2(G) can be realized as the Hilbert space of L^2-sections, of some twist of the spin bundle over the Riemannian symmetric space G/K, which belong to the kernel of the associated Dirac operator. Here K is a maximal compact subgroup of G. On the other hand, Dirac cohomology, introduced by Vogan in the late 1990’s, defines an invariant which can be used to detect the infinitesimal character of representations (theorem of Huang and Pandzic.Therefore it is important to study the behavior of the Dirac cohomology under functors involved in representation theory. A useful functor in representation theory of reductive groups is the so-called Θ-correspondence (or the Howe duality). Howe duality relates representations and characters of two Lie groups G_1 and G_2, viewed as closed subgroups of the metaplectic group Μ such that Z_M(G_1) = G_2 and Z_M(G_2) = G_1. In this talk, we will study the behavior of the Dirac cohomology under the Θ-correspondence in the case of complex pairs (G_1, G_2) viewed as real Lie groups. Joint work with G. Liu and S. Mehdi
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