English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let $G$ be a connected, reductive algebraic group over an algebraicallyclosed field $k$ of prime characteristic $p$ and $\mathfrak{g}=Lie(G)$. In thispaper, 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 byFriedlander and Parshall in [Friedlander E. M. and Parshall B. J., Deformationsof 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 resultof Jantzen in [Jantzen J. C., Subregular nilpotent representations of $sl_n$and $so_{2n+1}$, Math. Proc. Cambridge Philos. Soc. 126 (1999), 223-257].

A criterion for irreducibility of parabolic baby Verma modules of reductive Lie algebras