A criterion for irreducibility of parabolic baby Verma modules of reductive Lie algebras
| Autor: | Yu-Feng Yao, Bin Shu, Yi-Yang Li |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Verma module 010102 general mathematics Nilpotent orbit 17B10 17B20 17B35 17B50 Type (model theory) 01 natural sciences Algebraic group 0103 physical sciences Lie algebra FOS: Mathematics Irreducibility 010307 mathematical physics Representation Theory (math.RT) 0101 mathematics Special case Algebraically closed field Mathematics::Representation Theory Mathematics - Representation Theory Mathematics |
| Zdroj: | Journal of Algebra. 563:111-147 |
| ISSN: | 0021-8693 |
| Popis: | Let $G$ be a connected, reductive algebraic group over an algebraically closed field $k$ of prime characteristic $p$ and $\mathfrak{g}=Lie(G)$. In this paper, we study representations of $\mathfrak{g}$ with a $p$-character $\chi$ of standard Levi form. When $\mathfrak{g}$ is of type $A_n, B_n, C_n$ or $D_n$, a sufficient condition for the irreducibility of standard parabolic baby Verma $\mathfrak{g}$-modules is obtained. This partially answers a question raised by Friedlander and Parshall in [Friedlander E. M. and Parshall B. J., Deformations of Lie algebra representations, Amer. J. Math. 112 (1990), 375-395]. Moreover, as an application, in the special case that $\mathfrak{g}$ is of type $A_n$ or $B_n$, and $\chi$ lies in the sub-regular nilpotent orbit, we recover a result of Jantzen in [Jantzen J. C., Subregular nilpotent representations of $sl_n$ and $so_{2n+1}$, Math. Proc. Cambridge Philos. Soc. 126 (1999), 223-257]. Comment: 16 pages. Minor revision and references added |
| Databáze: | OpenAIRE |
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