On extensions of principal series representations

Gautam H. Borisagar; Asfak Soneji

doi:10.1007/s00013-025-02210-1

On extensions of principal series representations

Representation Theory 2026-02-10 v1

Authors: Gautam H. Borisagar , Asfak Soneji

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Abstract

We compute $\mathrm{Ext}^{1}_B(\chi_1,\chi_2)$ between two characters $\chi_1,\chi_2$ of a Borel subgroup $B$ of a split reductive group $G$ over a finite field $\mathbb{F}_q,$ and make an application to the calculation of $\mathrm{Ext}^1_G(\pi_1,\pi_2)$ between principal series representations $\pi_1,\pi_2$ of $G(\mathbb{F}_q).$

Keywords

principal series representations Borel subgroup Ext groups split reductive group finite field

Cite

@article{arxiv.2501.04301,
  title  = {On extensions of principal series representations},
  author = {Gautam H. Borisagar and Asfak Soneji},
  journal= {arXiv preprint arXiv:2501.04301},
  year   = {2026}
}

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