Kwangho Choiy, Southern Illinois University

Non-discrete tempered spectra for some simply-connected p-adic groups

Non-discrete tempered $L$-packets for $p$-adic groups are expected to consist of the irreducible constituents of parabolic induction from discrete $L$-packets of proper Levi subgroups. In this framework, we study the reducibility of the parabolic induction, and this talk will focus on the case of simply-connected $p$-adic groups by means of $R$-groups. After recalling the known cases of $SL(n),$ $SU(n),$ $Sp(2n),$ and their inner forms, we shall discuss unitary principal series of $Spin(n).$ We also mention expectations and obstacles towards a general simply-connected $p$-adic group. This is based on joint work with D. Goldberg and another with D. Ban and D. Goldberg.