Date: Friday, 18th November 2022 @4:35 pm
Venue: Ramanujan Hall
Speaker: T. N. Venkataramana, TIFR Mumbai
Title: Unipotent Generators for Higher Rank arithmetic Groups.
Abstract: Old results of Tits, Vaserstein, Raghunathan and myself say that the subgroup generated by elementary matrices, in any arithmetic higher rank group - namely the G(Z) of integer points of a simple algebraic group G defined over Q, is also arithmetic. The proofs rely on constructing a suitable completion of the group G(Q) of rational points and showing that this completion is a central extension of the (finite) adelic completion of G(Q). The other main ingredient of the proof relies on "Moore's uniqueness of reciprocity laws", which is used to deduce that
this extension is finite.
In this talk I describe a modification of the proof which shows that only the centrality is enough; the technically complicated second step may be avoided.