Theta-finite pro-Hermitian vector bundles from loop groups elements

Mathieu Dutour (University of Alberta)

28-Nov-2022, 19:00-20:00 (16 months ago)

Abstract: In the finite-dimensional situation, Lie's third theorem provides a correspondence between Lie groups and Lie algebras. Going from the latter to the former is the more complicated construction, requiring a suitable representation, and taking exponentials of the endomorphisms induced by elements of the group.

As shown by Garland, this construction can be adapted for some Kac-Moody algebras, obtained as (central extensions of) loop algebras. The resulting group is called a loop group. One also obtains a relevant infinite-rank Chevalley lattice, endowed with a metric. Recent work by Bost and Charles provide a natural setting, that of pro-Hermitian vector bundles and theta invariants, in which to study these objects related to loop groups. More precisely, we will see in this talk how to define theta-finite pro-Hermitian vector bundles from elements in a loop group. Similar constructions are expected, in the future, to be useful to study loop Eisenstein series for number fields.

This is joint work with Manish M. Patnaik.

combinatoricsnumber theory

Audience: researchers in the topic


Lethbridge number theory and combinatorics seminar

Organizers: FĂ©lix Baril Boudreau*, Ertan Elma
*contact for this listing

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