Algebraic analysis on scalar generalized Verma modules of Heisenberg parabolic type I.: An-series

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10333943" target="_blank" >RIV/00216208:11320/16:10333943 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00031-016-9414-5" target="_blank" >http://dx.doi.org/10.1007/s00031-016-9414-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00031-016-9414-5" target="_blank" >10.1007/s00031-016-9414-5</a>

Result language
angličtina
Original language name
Algebraic analysis on scalar generalized Verma modules of Heisenberg parabolic type I.: An-series
Original language description
In the present article, we combine some techniques in harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators ($mcal{D}$-modules), and reformulate the composition series and branching problems for objects in the Bernstein-Gelfand-Gelfand parabolic category $mcal{O}^mfrak{p}$ geometrically realized on certain orbits in the generalized flag manifolds. The general framework is then applied to the scalar generalized Verma modules supported on the closed Schubert cell of the generalized flag manifold $G/P$ for $G=SL(n+2,C)$ and $P$ the Heisenberg parabolic subgroup, and algebraic analysis gives a complete classification of $mfrak{g}'_r$-singular vectors for all $mfrak{g}'_r=mfrak{sl}(n-r+2,C),subset, mfrak{g}=mfrak{sl}(n+2,C)$, $n-r > 2$. A consequence of our results is that we classify $SL(n-r+2,C)$-covariant differential operators acting on homogeneous line bundles over the complexification of the odd dimensional CR-sphere $S^{2n+1}$ and valued in homogeneous vector bundles over the complexification of the CR-subspheres $S^{2(n-r)+1}$.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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