UNAM
Usted está aquí: Inicio / Actividades académicas / Seminarios en C.U. / Seminario de Representaciones de Álgebras / Actividades del Seminario de Representaciones de Álgebras / Kac-Moody groups - representations, projective resolutions and cosheaves

Kac-Moody groups - representations, projective resolutions and cosheaves

Ponente: Katerina Hristova
Institución: University of Warwick
Tipo de Evento: Investigación

Cuándo 14/11/2018
de 16:00 a 17:30
Dónde Salón 1 de seminarios
Agregar evento al calendario vCal
iCal

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.