University of Birmingham > Talks@bham > Birmingham and Warwick Algebra Seminar  > Brauer relations in finite groups

Brauer relations in finite groups

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If you have a question about this talk, please contact David Craven.

If G is a finite group, a Brauer relation is a pair of finite G-sets X, Y such that the complex permutation representations C[X] and C[Y] are isomorphic. Brauer noticed in the early 1950s that such pairs give rise to number fields that share many properties, but are, in general, not isomorphic. Later Brauer relations were used by Sunada to produce non-isometric isospectral manifolds (drums, whose shape you cannot hear), and most recently by the Dokchitser brothers in the theory of elliptic curves. Often, in order to apply Brauer relations in any of the above contexts, one needs to explicitly produce a suitable Brauer relation for a suitable group G. In joint work with Tim Dokchitser, we have completely classified all Brauer relations for all finite groups. I will explain what this classification looks like, giving lots of concrete examples along the way.

This talk is part of the Birmingham and Warwick Algebra Seminar series.

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