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- W3100459224 abstract "Let $p$ be a prime number and $Bbbk=bar{mathbb{F}}_p$, the algebraic closure of the finite field $mathbb{F}_p$ of $p$ elements. Let ${bf G}$ be a connected reductive group defined over $mathbb{F}_p$ and ${bf B}$ be a Borel subgroup of ${bf G}$ (not necessarily defined over $mathbb{F}_p$). We show that for each (one-dimensional) character $theta$ of ${bf B}$ (not necessarily rational), there is a unique (up to isomorphism) irreducible $Bbbk{bf G}$-module $mathbb{L}(theta)$ containing $theta$ as a $Bbbk{bf B}$-submodule, and moreover, $mathbb{L}(theta)$ is isomorphic to a parabolic induction from a finite-dimensional irreducible $Bbbk{bf L}$-module for some Levi subgroup ${bf L}$ of ${bf G}$. Thus, we have classified and constructed all (abstract) irreducible $Bbbk{bf G}$-modules with ${bf B}$-stable line (i.e. an one-dimensional $Bbbk{bf B}$-submodule). As a byproduct, we give a new proof of a result of Borel and Tits on the classification of finite-dimensional irreducible $Bbbk{bf G}$-modules." @default.
- W3100459224 created "2020-11-23" @default.
- W3100459224 creator A5043094856 @default.
- W3100459224 date "2020-11-08" @default.
- W3100459224 modified "2023-10-14" @default.
- W3100459224 title "Irreducible Modules of Reductive Groups with Borel-stable Line" @default.
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- W3100459224 doi "https://doi.org/10.48550/arxiv.2011.04115" @default.
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