Journal of Lie Theory

no. 2
Homomorphisms of Generalized Verma Modules, BGG Parabolic Category Op and Juhl's Conjecture
Journal of Lie Theory, Volume 22 (2012) no. 2, pp. 541-555
\def\g{{\frak g}} \def\p{{\frak p}} Let ${\cal M}_\lambda(\g,\p)$, ${\cal M}_\mu(\g^\prime, \p^\prime)$ be the generalized Verma modules for $\g={\rm so}(p+1,q+1), \g^\prime={\rm so}(p,q+1)$ induced from characters $\lambda$ ,$\mu$ of the standard maximal parabolic (conformal) subalgebras $\p$, $\p^\prime=\g^\prime\cap\p$. Motivated by questions about the existence of invariant differential operators in conformal geometry, we explain, reformulate and prove an extended version of Juhl's conjecture on the structure of ${\cal U}(\g^\prime)$-homomorphisms of generalized Verma modules from ${\cal M}_\lambda(\g^\prime,\p^\prime)$ to ${\cal M}_\mu(\g,\p)$. The answer has a natural formulation as a branching problem in the BGG parabolic category ${\cal O}^{\p^\prime}$ rather than the set of generalized Verma modules alone.
DOI: 10.5802/jolt.681
Classification: 22E47, 17B10, 13C10
Keywords: Branching rules, generalized Verma modules, BGG parabolic category Op, Juhl's conjectures 
@article{JOLT_2012_22_2_a10,
     author = {P. Somberg},
     title = {Homomorphisms of {Generalized} {Verma} {Modules,} {BGG} {Parabolic} {Category} {O\protect\textsuperscript{p}} and {Juhl's} {Conjecture}},
     journal = {Journal of Lie Theory},
     pages = {541--555},
     year = {2012},
     volume = {22},
     number = {2},
     doi = {10.5802/jolt.681},
     zbl = {1246.22018},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.681/}
}
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%A P. Somberg
%T Homomorphisms of Generalized Verma Modules, BGG Parabolic Category Op and Juhl's Conjecture
%J Journal of Lie Theory
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P. Somberg. Homomorphisms of Generalized Verma Modules, BGG Parabolic Category Op and Juhl's Conjecture. Journal of Lie Theory, Volume 22 (2012) no. 2, pp. 541-555. doi: 10.5802/jolt.681

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