Glasnik Matematicki, Vol. 49, No. 1 (2014), 123-161.

IRREDUCIBILITY CRITERION FOR REPRESENTATIONS INDUCED BY ESSENTIALLY UNITARY ONES (CASE OF NON-ARCHIMEDEAN GL(n, 𝒜))

Marko Tadić

Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
e-mail: tadic@math.hr


Abstract.   Let 𝒜 be a finite dimensional central division algebra over a local non-archimedean field F. Fix any parabolic subgroup P of GL(n,𝒜) and a Levi factor M of P. Let π be an irreducible unitary representation of M and φ a (not necessarily unitary) character of M. We give an explicit necessary and sufficient condition for the parabolically induced representation

IndPGL(n,𝒜)(φπ)
to be irreducible.

2010 Mathematics Subject Classification.   22E50.

Key words and phrases.   Non-archimedean local fields, division algebras, general linear groups, Speh representations, parabolically induced representations, reducibility, unitarizability.


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DOI: 10.3336/gm.49.1.11


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