Degenerate principal series for exceptional p -adic groups.

Abstract

This is a report on normalized inductions from characters of maximal parabolic subgroups of exceptional p-adic groups. Matrix realization can be used to get the results for a group of type <italic>G</italic>₂ (7 by 7 matrices) and a group of type <italic>F</italic>₄ (26 by 26 matrices). However, using the description of the maximal split torus in terms of coroots, we can do the same computation without a matrix realization. The two main methods in my work are Jacquet module techniques and Hecke algebra isomorphisms. The Jacquet module technique leads to a reducibility criterion, which is applied to the regular cases. For the nonregular cases, the Hecke algebra isomorphism provides a way of reducing reducibility questions to the classical groups.