Branching laws for Verma modules and applications in parabolic geometry. I

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10315173" target="_blank" >RIV/00216208:11320/15:10315173 - isvavai.cz</a>

Výsledek na webu

<a href="http://10.1016/j.aim.2015.08.020" target="_blank" >http://10.1016/j.aim.2015.08.020</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aim.2015.08.020" target="_blank" >10.1016/j.aim.2015.08.020</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Branching laws for Verma modules and applications in parabolic geometry. I

Popis výsledku v původním jazyce

We initiate a new study of differential operators with symmetries and combine this with the study of branching laws for Verma modules of reductive Lie algebras. By the criterion for discretely decomposable and multiplicity-free restrictions of generalized Verma modules (T. Kobayashi (2012) [22]), we are brought to natural settings of parabolic geometries for which there exist unique equivariant differential operators to submanifolds. Then we apply a new method (F-method) relying on the Fourier transformto find singular vectors in generalized Verma modules, which significantly simplifies and generalizes many preceding works. In certain cases, it also determines the Jordan-Hölder series of the restriction for singular parameters. The F-method yields anexplicit formula of such unique operators, for example, giving an intrinsic and new proof of Juhl's conformally invariant differential operators (Juhl (2009) [16]) and its generalizations to spinor bundles. This article is the first in th

Název v anglickém jazyce

Branching laws for Verma modules and applications in parabolic geometry. I

Popis výsledku anglicky

We initiate a new study of differential operators with symmetries and combine this with the study of branching laws for Verma modules of reductive Lie algebras. By the criterion for discretely decomposable and multiplicity-free restrictions of generalized Verma modules (T. Kobayashi (2012) [22]), we are brought to natural settings of parabolic geometries for which there exist unique equivariant differential operators to submanifolds. Then we apply a new method (F-method) relying on the Fourier transformto find singular vectors in generalized Verma modules, which significantly simplifies and generalizes many preceding works. In certain cases, it also determines the Jordan-Hölder series of the restriction for singular parameters. The F-method yields anexplicit formula of such unique operators, for example, giving an intrinsic and new proof of Juhl's conformally invariant differential operators (Juhl (2009) [16]) and its generalizations to spinor bundles. This article is the first in th

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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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

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

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

2015

Číslo periodika v rámci svazku

285

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

57

Strana od-do

1-57

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-84942163856