### Representations of complete Kac-Moody groups

Algebra and Geometry Seminar

25th April 2018, 2:30 pm – 3:30 pm

Howard House, 4th Floor Seminar Room

Complete Kac-Moody groups are locally compact totally disconnected topological groups with a BN-pair structure. Thus, on one side they have a Bruhat-Tits building which they naturally act on, and on another, due to their topological properties, they admit so called “smooth representations”. We explain what those are and using the action on the building we explain how to deduce properties about the projective dimension of the category of smooth representations and show how to construct explicit projective resolutions of objects. We explain how the approach can be generalised to groups of Kac-Moody type, i.e., which admit a generalised BN-pair structure, and explain what the relative building is. If time permits, we explain the difficulties one encounters if one wishes to construct resolutions with finitely generated projectives. Joint work with Dmitriy Rumynin.

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