Relative BGG sequences; II. BGG machinery and invariant operators
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10370120" target="_blank" >RIV/00216208:11320/17:10370120 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aim.2017.09.016" target="_blank" >http://dx.doi.org/10.1016/j.aim.2017.09.016</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2017.09.016" target="_blank" >10.1016/j.aim.2017.09.016</a>
Alternative languages
Result language
angličtina
Original language name
Relative BGG sequences; II. BGG machinery and invariant operators
Original language description
For a real or complex semisimple Lie group G and two nested parabolic subgroups Q subset of P subset of G, we study parabolic geometries of type (G, Q). Associated to the group P, we introduce the classes of relative natural bundles and of relative tractor bundles and construct some basic invariant differential operators on such bundles. We define a (rather weak) notion of "compressability" for operators acting on relative differential forms with values in a relative tractor bundle. Then we develop a general machinery which converts a compressable operator to an operator on bundles associated to completely reducible representations on relative Lie algebra homology groups. Applying this machinery to a specific compressable invariant differential operator of order one, we obtain a relative version of BGG (Bernstein-Gelfand-Gelfand) sequences. All our constructions apply in the case P = G, producing new and simpler proofs in the case of standard BGG sequences. We characterize cases in which the relative BGG sequences are complexes or even fine resolutions of certain sheaves and describe these sheaves. We show that this gives constructions of new invariant differential operators as well as of new subcomplexes in certain curved BGG sequences. The results are made explicit in the case of generalized path geometries.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
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)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Mathematics
ISSN
0001-8708
e-ISSN
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Volume of the periodical
320
Issue of the periodical within the volume
Neuveden
Country of publishing house
US - UNITED STATES
Number of pages
54
Pages from-to
1009-1062
UT code for WoS article
000413884400029
EID of the result in the Scopus database
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