Glasnik Matematicki, Vol. 55, No. 2 (2020), 203-235.

ON REPRESENTATIONS OF REDUCTIVE P-ADIC GROUPS OVER ℚ-ALGEBRAS

Goran Muić

Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
e-mail: gmuic@math.hr

Abstract.   In this paper we study certain category of smooth modules for reductive p-adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a ℚ-algebra. We prove some fundamental results in these settings, and as an example we give a classification of admissible unramified irreducible representations using the reduction to the complex case.

2010 Mathematics Subject Classification.   11E70, 22E50

Key words and phrases.   Reductive p-adic groups, ℚ-admissible representations, Hecke algebras

Full text (PDF) (free access)

https://doi.org/10.3336/gm.55.2.04

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