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On an algorithm to compute derivatives

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Abstract

In this paper, we complete Jantzen’s algorithm to compute the highest derivatives of irreducible representations of p-adic odd special orthogonal groups or symplectic groups. As an application, we give some examples of the Langlands data of the Aubert duals of irreducible representations, which are in the integral reducibility case.

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Acknowledgements

The author is grateful to Professor Alberto Mínguez for telling the notion of derivatives and several results. He wishes to thank Professor Chris Jantzen for allowing him to work on this topic. Thanks are also due to the referee for the careful readings and the helpful comments. This work was supported by JSPS KAKENHI Grant No. 19K14494.

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

    Hiraku Atobe

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Atobe, H. On an algorithm to compute derivatives. manuscripta math. 167, 721–763 (2022). https://doi.org/10.1007/s00229-021-01285-8

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