Relative BGG sequences; II. BGG machinery and invariant operators

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Relative BGG sequences; II. BGG machinery and invariant operators

Popis výsledku v původním jazyce

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 &quot;compressability&quot; 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.

Název v anglickém jazyce

Relative BGG sequences; II. BGG machinery and invariant operators

Popis výsledku anglicky

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 &quot;compressability&quot; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advances in Mathematics

ISSN

0001-8708

e-ISSN

—

Svazek periodika

320

Číslo periodika v rámci svazku

Neuveden

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

54

Strana od-do

1009-1062

Kód UT WoS článku

000413884400029

EID výsledku v databázi Scopus

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