Construction of local <i>A</i>-packets-Reference-Cited by-同舟云学术

Construction of local A-packets

Published:2022-06-29 Issue:790 Volume:2022 Page:1-51
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Atobe Hiraku¹

Affiliation:

1. Department of Mathematics , Hokkaido University , Kita 10, Nishi 8, Kita-Ku , Sapporo , Hokkaido, 060-0810 , Japan

Abstract

Abstract In the present paper, we reformulate Mœglin’s explicit construction of local A-packets of split odd special orthogonal groups and symplectic groups. By this reformulation together with results of the previous paper with Mínguez, we can compute the A-packets explicitly. Also, we give a non-vanishing criterion of our parametrization, and an algorithm to compute certain derivatives. Finally, we prove a formula for the Aubert duals of irreducible representations of Arthur type.

Funder

Japan Society for the Promotion of Science

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2022-0030/pdf

Reference23 articles.

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2. H. Atobe and A. Mínguez, The explicit Zelevinsky–Aubert duality, preprint (2020), https://arxiv.org/abs/2008.05689v2.

3. A.-M. Aubert, Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d'un groupe réductif p-adique, Trans. Amer. Math. Soc. 347 (1995), no. 6, 2179-2189

4. erratum, Trans. Amer. Math. Soc. 348, (1996), 4687-4690.

5. I. Badulescu, E. Lapid and A. Mínguez, Une condition suffisante pour l’irréductibilité d’une induite parabolique de GL ⁢ ( m , D ) {\rm GL}(m,{\rm D}) , Ann. Inst. Fourier (Grenoble) 63 (2013), no. 6, 2239–2266.

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