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Presentation of an Iwasawa algebra: The pro-p Iwahori of simple, simply connected, split groups

Part of: Lie groups Algebraic number theory: global fields Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 January 2025

Aranya Lahiri  and
Jishnu Ray Open the ORCID record for Jishnu Ray [Opens in a new window]
Aranya Lahiri
Affiliation:
Department of Mathematics, Indiana University, Bloomington, 831 E 3rd St, Bloomington, IN 47405, United States and University of California San Diego, 9500 Gilman Dr., La Jolla, CA 92093, United States e-mail: arlahiri@ucsd.edu
Jishnu Ray*
Affiliation:
Department of Mathematics, Harish Chandra Research Institute, A CI of Homi Bhabha National Institute, Chhatnag Road, Jhunsi, Prayagraj (Allahabad) 211 019, India
*
e-mail: jishnuray@hri.res.in jishnuray1992@gmail.com
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Abstract

In this article, we generalize results of Clozel and Ray (for $SL_2$ and $SL_n$, respectively) to give explicit ring-theoretic presentation in terms of a complete set of generators and relations of the Iwasawa algebra of the pro-p Iwahori subgroup of a simple, simply connected, split group $\mathbf {G}$ over ${{\mathbb Q}_p}$.

Keywords

Iwasawa algebrapro-p Iwahorireductive groups

MSC classification

Primary: 11R23: Iwasawa theory
Secondary: 20E25: Local properties 22E50: Representations of Lie and linear algebraic groups over local fields
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 18
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

The second author is supported by the Inspire Research Grant, Department of Science and Technology, Govt. of India.

References

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