Conformal symmetry breaking differential operators on differential forms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10423772" target="_blank" >RIV/00216208:11320/20:10423772 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=nUrspV0NdV" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=nUrspV0NdV</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/memo/1304" target="_blank" >10.1090/memo/1304</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Conformal symmetry breaking differential operators on differential forms

Popis výsledku v původním jazyce

We study conformal symmetry breaking differential operators which map differential forms on Rn to differential forms on a codimension one subspace Rn-1. These operators are equivariant with respect to the conformal Lie algebra of the subspace Rn-1. They correspond to homomorphisms of generalized Verma modules for so(n, 1) into generalized Verma modules for so(n+1, 1) both being induced from fundamental form representations of a parabolic subalgebra. We apply the F-method to derive explicit formulas for such homomorphisms. In particular, we find explicit formulas for the generators of the intertwining operators of the related branching problems restricting generalized Verma modules for so(n+1, 1) to so(n, 1). As consequences, we derive closed formulas for all conformal symmetry breaking differential operators in terms of the first-order operators d, δ, - d and -δ and certain hypergeometric polynomials. A dominant role in these studies is played by two infinite sequences of symmetry breaking differential operators which depend on a complex parameter λ. Their values at special values of λ appear as factors in two systems of factorization identities which involve the Branson-Gover operators of the Euclidean metrics on Rn and Rn-1 and the operators d, δ, - d and -δ as factors, respectively. Moreover, they naturally recover the gauge companion and Q-curvature operators of the Euclidean metric on the subspace Rn-1, respectively.

Název v anglickém jazyce

Conformal symmetry breaking differential operators on differential forms

Popis výsledku anglicky

We study conformal symmetry breaking differential operators which map differential forms on Rn to differential forms on a codimension one subspace Rn-1. These operators are equivariant with respect to the conformal Lie algebra of the subspace Rn-1. They correspond to homomorphisms of generalized Verma modules for so(n, 1) into generalized Verma modules for so(n+1, 1) both being induced from fundamental form representations of a parabolic subalgebra. We apply the F-method to derive explicit formulas for such homomorphisms. In particular, we find explicit formulas for the generators of the intertwining operators of the related branching problems restricting generalized Verma modules for so(n+1, 1) to so(n, 1). As consequences, we derive closed formulas for all conformal symmetry breaking differential operators in terms of the first-order operators d, δ, - d and -δ and certain hypergeometric polynomials. A dominant role in these studies is played by two infinite sequences of symmetry breaking differential operators which depend on a complex parameter λ. Their values at special values of λ appear as factors in two systems of factorization identities which involve the Branson-Gover operators of the Euclidean metrics on Rn and Rn-1 and the operators d, δ, - d and -δ as factors, respectively. Moreover, they naturally recover the gauge companion and Q-curvature operators of the Euclidean metric on the subspace Rn-1, respectively.

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

2020

Kód důvěrnosti údajů

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

Název periodika

Memoirs of the American Mathematical Society

ISSN

0065-9266

e-ISSN

—

Svazek periodika

2020

Číslo periodika v rámci svazku

1304

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

122

Strana od-do

1-122

Kód UT WoS článku

000621025000001

EID výsledku v databázi Scopus

2-s2.0-85101432574