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Types for elliptic non-discrete series representations of \(SL_N(F)\), \(N\) prime and \(F\) a \(p\)-adic field. (English) Zbl 0909.22032

Let \(F\) be a \(p\)-adic field and \(l\) a prime. Set \(G=SL_l(F)\). An elliptic representation of \(G\) is an irreducible representation \(\pi\) with character \(\theta\) such that \(\theta\) is nonzero on some compact Cartan. Discrete series representations are elliptic. In this paper a classification is given for the elliptic, nondiscrete series representations of \(G\) by the method of types, that is, by restriction to compact open subgroups. An explicit construction of certain types is given and their Hecke algebras are determined. The main result states that a nondiscrete series representation is elliptic if and only if it contains one of the types constructed.

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
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