On regular square integrable representations of \(p\)-adic groups. (English) Zbl 0903.22008

Tadić, Marko

Am. J. Math. 120, No. 1, 159-210 (1998).

Given a local nonarchimedean field of odd characteristic, the author constructs regular irreducible square integrable representations of the groups \(GSp(n,F)\), \(Sp(n,F)\) and \(SO(2n+1,F)\) and under an assumption proves that all such representations should come from such a construction. He then obtains a number of general results about places where square integrable representations can appear in parabolically induced representations. For example, it is shown that in irreducible cuspidal representations of general linear groups, only the self-contragredient ones play a role in the construction of square integrable representations of the above groups. The author also shows that there are nondegenerate standard modules of classical groups containing degenerate irreducible representations and uses the regular square integrable representations described above to study some basic properties of Whittaker models.

Reviewer: Min Ho Lee (Cedar Falls)

MSC:

22E50

Representations of Lie and linear algebraic groups over local fields

Keywords:

square integrable representations; \(p\)-adic groups; cuspidal representations; Whittaker models