Colloquium abstracts

Jeff Adler
IISER, Pune
July 5, 2018

Multiplicity upon restriction to the derived subgroup:  If G is the group of rational points of an algebraic group over a locally compact field, and H contains the derived subgroup of G, then one expects the representation theories of G and H to be closely related. But how closely? An irreducible representation of G, when restricted to H, decomposes as a finite direct sum of irreducible representations, all occurring with the same multiplicity, and part of the answer is to understand this multiplicity. In the case of p-adic groups, I present a conjectural formula for this multiplicity in terms of Langlands parameters, together with a heuristic for why it should be true. Finally, I compute that the multiplicity is 1 for most classical groups, and give an example of multiplicity two. The above is joint work with Dipendra Prasad.