Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 405-423.

JACQUET TENSORS

Dubravka Ban

Abstract.   Let G be a split reductive p-adic group. The category of admissible p-adic Banach space representations of G is equivalent to the corresponding category of finitely generated Iwasawa modules, via the duality map V ↦ V'. In this paper, we define certain tensors on Iwasawa modules, which are intended to play the role of Jacquet modules. We describe some properties of Jacquet tensors and show how they can be applied to the study of principal series representations.

2020 Mathematics Subject Classification.   22E50, 11F70.

Key words and phrases.   p-adic Banach space representations, p-adic groups, Iwasawa modules, Jacquet modules.

DOI: https://doi.org/10.21857/mjrl3uo0x9

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