Startseite Modular representations of GL2(𝔽𝑞) using calculus
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Modular representations of GL2(𝔽𝑞) using calculus

  • Eknath Ghate ORCID logo und Arindam Jana EMAIL logo
Veröffentlicht/Copyright: 8. Januar 2025

Abstract

We show that certain modular induced representations of GL 2 ( F q ) can be written as cokernels of operators acting on symmetric power representations of GL 2 ( F q ) . When the induction is from the Borel subgroup or the anisotropic torus, the operators involve multiplication by newly defined twisted Dickson polynomials or twisted Serre operators, respectively. Our isomorphisms are explicitly defined using differential operators. As a corollary, we improve some periodicity results for quotients in the theta filtration.

MSC 2020: 20C33; 20C20

Acknowledgements

We thank A. Chitrao, C. Khare and S. Varma for useful discussions. Both authors thank the referee for many useful comments and suggestions. The first author thanks ANU, Canberra for its hospitality during March 2024.

  1. Communicated by: Freydoon Shahidi

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Received: 2023-12-18
Revised: 2024-11-08
Published Online: 2025-01-08
Published in Print: 2025-06-01

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