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.
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.