1Faculty of Science, University of Zagreb, Bijenicka cesta 30, 10 000 Zagreb, Croatia 2Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kacica-Miosica 26, 10 000 Zagreb, Croatia
Journal of Lie Theory, Tome 28 (2018) no. 4, pp. 1149-1164
\newcommand{\Sp}{\operatorname{Sp}} \newcommand{\mbbC}{\mathbb{C}} \newcommand{\GL}{\operatorname{GL}} We construct exact sequences of invariant differential operators acting on sections of certain homogeneous vector bundles in singular infinitesimal character, over the isotropic $2$-Grassmannian. This space is equal to $G/P$, where $G$ is $\Sp(2n,\mbbC)$, and $P$ its standard parabolic subgroup having the Levi factor $\GL(2,\mbbC) \times \Sp(2n-4,\mbbC)$. The constructed sequences are analogues of the Bernstein-Gelfand-Gelfand resolutions. We do this by considering the Penrose transform over an appropriate double fibration. The result differs from the Hermitian situation.
1
Faculty of Science, University of Zagreb, Bijenicka cesta 30, 10 000 Zagreb, Croatia
2
Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kacica-Miosica 26, 10 000 Zagreb, Croatia
Denis Husadzic; Rafael Mrden. Singular BGG Complexes Over Isotropic 2-Grassmannian. Journal of Lie Theory, Tome 28 (2018) no. 4, pp. 1149-1164. http://geodesic.mathdoc.fr/item/JOLT_2018_28_4_a11/
@article{JOLT_2018_28_4_a11,
author = {Denis Husadzic and Rafael Mrden},
title = {Singular {BGG} {Complexes} {Over} {Isotropic} {2-Grassmannian}},
journal = {Journal of Lie Theory},
pages = {1149--1164},
year = {2018},
volume = {28},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2018_28_4_a11/}
}
TY - JOUR
AU - Denis Husadzic
AU - Rafael Mrden
TI - Singular BGG Complexes Over Isotropic 2-Grassmannian
JO - Journal of Lie Theory
PY - 2018
SP - 1149
EP - 1164
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2018_28_4_a11/
ID - JOLT_2018_28_4_a11
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%T Singular BGG Complexes Over Isotropic 2-Grassmannian
%J Journal of Lie Theory
%D 2018
%P 1149-1164
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%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2018_28_4_a11/
%F JOLT_2018_28_4_a11
