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Arithmetic aspects of infinite-dimensional groups

4:00 pm Thursday, October 27, 2011
Daniel Allcock (UT Austin)

The most-studied infinite-dimensional groups are the loop groups--the space of maps from the circle to a Lie group--and their central extensions and generalizations, Kac-Moody groups. Physicists are the major "consumer" of these groups, and naturally they think of them as real Lie groups. But just as one can think about SL(n,Z) as a natural subgroup of SL(n,R), one can ask what the natural integer form of the exceptional Lie group E8 is, or indeed of loop groups or even more exotic groups, like "E10". In some cases there are unique best answers, and in others it's not yet clear what that would even mean. We will discuss old and new results about these groups.

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