Let $\mathfrak{g}$ be an exceptional complex simple Lie algebra and $\mathfrak{q}$ be a parabolic subalgebra. A generalized Verma module $M$ is called a scalar generalized Verma module if it is induced from a one-dimensional representation of $\mathfrak{q}$. In this paper, we will determine the first diagonal-reducible point of scalar generalized Verma modules associated to minimal parabolic subalgebras of exceptional Lie algebras by computing explicitly the Gelfand–Kirillov (GK) dimension of the corresponding highest weight modules.
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Keywords: Gelfand–Kirillov dimension, minimal parabolic subalgebra, exceptional type, PyCox
Jiang, Jing 1 ; Wu, Siying 1
Jiang, Jing; Wu, Siying. Reducibility of scalar generalized Verma modules of minimal parabolic type II. Journal of Lie Theory, Volume 36 (2026) no. 2-3, pp. 529-559. doi: 10.5802/jolt.1439
@article{10_5802_jolt_1439,
author = {Jiang, Jing and Wu, Siying},
title = {Reducibility of scalar generalized {Verma} modules of minimal parabolic {type~II}},
journal = {Journal of Lie Theory},
pages = {529--559},
year = {2026},
publisher = {XXXX},
volume = {36},
number = {2-3},
doi = {10.5802/jolt.1439},
language = {en},
url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1439/}
}
TY - JOUR AU - Jiang, Jing AU - Wu, Siying TI - Reducibility of scalar generalized Verma modules of minimal parabolic type II JO - Journal of Lie Theory PY - 2026 SP - 529 EP - 559 VL - 36 IS - 2-3 PB - XXXX UR - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1439/ DO - 10.5802/jolt.1439 LA - en ID - 10_5802_jolt_1439 ER -
%0 Journal Article %A Jiang, Jing %A Wu, Siying %T Reducibility of scalar generalized Verma modules of minimal parabolic type II %J Journal of Lie Theory %D 2026 %P 529-559 %V 36 %N 2-3 %I XXXX %U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1439/ %R 10.5802/jolt.1439 %G en %F 10_5802_jolt_1439
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