Journal of Lie Theory

no. 4
Singular BGG Complexes Over Isotropic 2-Grassmannian
Journal of Lie Theory, Volume 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.
DOI: 10.5802/jolt.1043
Classification: 58J10, 53C28, 53A55
Keywords: Bernstein-Gelfand-Gelfand (BGG) complexes, singular infinitesimal character, isotropic 2-Grassmannian, invariant differential operators, Penrose transform 
@article{JOLT_2018_28_4_a11,
     author = {D. Husadzic and R. Mrden},
     title = {Singular {BGG} {Complexes} {Over} {Isotropic} {2-Grassmannian}},
     journal = {Journal of Lie Theory},
     pages = {1149--1164},
     year = {2018},
     volume = {28},
     number = {4},
     doi = {10.5802/jolt.1043},
     zbl = {1406.58016},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1043/}
}
TY  - JOUR
AU  - D. Husadzic
AU  - R. 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  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1043/
DO  - 10.5802/jolt.1043
ID  - JOLT_2018_28_4_a11
ER  - 
%0 Journal Article
%A D. Husadzic
%A R. Mrden
%T Singular BGG Complexes Over Isotropic 2-Grassmannian
%J Journal of Lie Theory
%D 2018
%P 1149-1164
%V 28
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1043/
%R 10.5802/jolt.1043
%F JOLT_2018_28_4_a11
D. Husadzic; R. Mrden. Singular BGG Complexes Over Isotropic 2-Grassmannian. Journal of Lie Theory, Volume 28 (2018) no. 4, pp. 1149-1164. doi: 10.5802/jolt.1043

Cited by Sources: