Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 3-48.

THE TADIĆ PHILOSOPHY: AN OVERVIEW OF THE GUIDING PRINCIPLES AND UNDERLYING IDEAS IN THE WORK OF MARKO TADIĆ

Neven Grbac and Marcela Hanzer

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

Abstract.   This paper provides an overview of the guiding principles and underlying ideas in the work of Marko Tadić. His research is mostly concerned with the representation theory of reductive groups over local fields. From the authors' perspective, the most important guiding principles in his work are the essential simplicity of harmonic analysis, even in the non-commutative non-compact case, the Lefschetz principle saying that the representation theory over archimedean and non-archimedean fields should be studied in a unified way, and the principle of comparison of Jacquet modules. Besides these, the most prominent and fruitful ideas are the structural external approach to the unitary dual, the unitarizability along the lines, the use of topology of various duals to get information in harmonic analysis and arithmetic of the underlying group, and the interplay between unitarizability and Arthur packets. All these principles and ideas are the subject of this paper.

2020 Mathematics Subject Classification.   22E50, 22E55, 11F70, 01A65, 01A70.

Key words and phrases.   Work of Marko Tadić, representation theory of p-adic groups, harmonic analysis, Lefschetz principle, parabolic induction, unitarizability, Arthur packets.

DOI: https://doi.org/10.21857/mzvkpto109

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