Kac-Moody groups - representations, projective resolutions and cosheaves
Institución: University of Warwick
Tipo de Evento: Investigación
Cuándo |
14/11/2018 de 16:00 a 17:30 |
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Dónde | Salón 1 de seminarios |
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Kac-Moody groups - representations, projective resolutions and cosheaves
Abstract: Complete Kac-Moody groups are locally compact totally disconnected topological groups which also have a (B,N)-pair structure. Thus, similarly to p-adic groups, when interested in their representation theory, one can look at their so-called "smooth" representations. These are representations in the usual sense with an extra continuity condition. Our investigation of the representation theory of Kac-Moody groups aims to combine two known, in the case of p-adic groups, lines of inquiry. In 1992 Bernstein studies smooth representations of p-adic groups by looking at their action on the associated Bruhat-Tits building. Later on, Schneider and Stuhler add to this - they study representations by looking at equivariant cosheaves on the building. In this talk we explain how this can be generalised to the setting of complete Kac-Moody groups, thus bringing new information about their representations to the table. In particular, we give a bound on the projective dimension of their category of smooth representations, explain how to construct projective resolutions therein, and show how these help us in understanding homological duality theory. Joint work with Dr Dmitriy Rumynin.