Parabolic conformally symplectic structures III; Invariant differential operators and complexes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10403841" target="_blank" >RIV/00216208:11320/19:10403841 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=zpw-iLDuIn" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=zpw-iLDuIn</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.25537/dm.2019v24.2203-2240" target="_blank" >10.25537/dm.2019v24.2203-2240</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parabolic conformally symplectic structures III; Invariant differential operators and complexes

Popis výsledku v původním jazyce

This is the last part of a series of articles on a family of geometric structures (PACS-structures) which all have an underlying almost conformally symplectic structure. While the first part of the series was devoted to the general study of these structures, the second part focused on the case that the underlying structure is conformally symplectic (PCS-structures). In that case, we obtained a close relation to parabolic contact structures via a concept of parabolic contactification. It was also shown that special symplectic connections (and thus all connections of exotic symplectic holonomy) arise as the canonical connection of such a structure. In this last part, we use parabolic contactifications and constructions related to Bernstein-Gelfand-Gelfand (BGG) sequences for parabolic contact structures, to construct sequences of differential operators naturally associated to a PCS-structure. In particular, this gives rise to a large family of complexes of differential operators associated to a special symplectic connection. In some cases, large families of complexes for more general instances of PCS-structures are obtained.

Název v anglickém jazyce

Parabolic conformally symplectic structures III; Invariant differential operators and complexes

Popis výsledku anglicky

This is the last part of a series of articles on a family of geometric structures (PACS-structures) which all have an underlying almost conformally symplectic structure. While the first part of the series was devoted to the general study of these structures, the second part focused on the case that the underlying structure is conformally symplectic (PCS-structures). In that case, we obtained a close relation to parabolic contact structures via a concept of parabolic contactification. It was also shown that special symplectic connections (and thus all connections of exotic symplectic holonomy) arise as the canonical connection of such a structure. In this last part, we use parabolic contactifications and constructions related to Bernstein-Gelfand-Gelfand (BGG) sequences for parabolic contact structures, to construct sequences of differential operators naturally associated to a PCS-structure. In particular, this gives rise to a large family of complexes of differential operators associated to a special symplectic connection. In some cases, large families of complexes for more general instances of PCS-structures are obtained.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-01171S" target="_blank" >GA17-01171S: Invariantní diferenciální operátory a jejich aplikace v geometrickém modelování a v teorii optimálního řízení</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Documenta Mathematica

ISSN

1431-0643

e-ISSN

—

Svazek periodika

2019

Číslo periodika v rámci svazku

24

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

38

Strana od-do

2203-2240

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85078065710