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Journal of Lie Theory 25 (2015), No. 1, 147--183
Copyright Heldermann Verlag 2015

On the Reducibility Points beyond the Ends of Complementary Series of p-adic General Linear Groups

Marko Tadic
Department of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, Croatia

We consider the reducibility points beyond the ends of complementary series of general linear groups over a p-adic field, which start with Speh representations. We describe explicitly the composition series of the representations at these reducibility points. They are multiplicity one representations, and they can be of arbitrary length. We give Langlands parameters of all the irreducible subquotients and determine the lattice of subrepresentations.

Keywords: Non-archimedean local fields, general linear groups, Speh representations, parabolically induced representations, reducibility, composition series, unitarizability.

MSC: 22E50

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