SOME BOUNDS ON UNITARY DUALS OF CLASSICAL GROUPS - NON-ARCHIMEDEN CASE

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TADIC M.

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Journal Paper

Paper Information

Journal: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY Year:2017 | Volume:43 | Issue:4 SPECIAL ISSUE Page(s): 405-433

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Title

SOME BOUNDS ON UNITARY DUALS OF CLASSICAL GROUPS - NON-ARCHIMEDEN CASE

Author(s)

TADIC M.

Keywords

IRREDUCIBLE UNITARY REPRESENTATIONS

PARABOLIC INDUCTION

UNI-TARY DUAL

AUTOMORPHIC DUAL

Abstract

We rst give bounds for domains where the unitarizabile sub-quotients can show up in the parabolically induced representations of clas-sical groups over ap -adic eld of characteristic 0. Roughly, they can show up only if the central character of the inducing irreducible cuspidal repre-sentation is dominated by the square root of the modular character of the minimal parabolic subgroup. For unitarizable subquotients supported by a xed parabolic subgroup, or in a specic Bernstein component, a more precise bound is given.For the reductive groups of rank at least two, the trivial representation is always isolated in the unitary dual (D. Kazhdan). Still, we may ask if the level of isolation is higher in the case of the automorphic duals, as it is a case in the rank one. We show that the answer is negative to this question for symplecticp -adic groups.

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