Homogeneous Hermitian holomorphic vector bundles and operators in the Cowen-Douglas class over the poly-disc

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F22%3AA0000110" target="_blank" >RIV/47813059:19610/22:A0000110 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022247X22000452" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X22000452</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2022.126031" target="_blank" >10.1016/j.jmaa.2022.126031</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Homogeneous Hermitian holomorphic vector bundles and operators in the Cowen-Douglas class over the poly-disc

Popis výsledku v původním jazyce

In this article, we obtain two sets of results. The first set of results are for the case of the bi-disc while the second set of results describe in part, which of these carry over to the general case of the poly-disc. A classification of irreducible hermitian holomorphic vector bundles over D-2, homogeneous with respect to Mob x Mob, is obtained assuming that the associated representations are multiplicity-free. Among these the ones that give rise to an operator in the Cowen-Douglas class of D-2 of rank 1, 2 or 3 are determined. Any hermitian holomorphic vector bundle of rank 2 over D-n, homogeneous with respect to the n-fold direct product of the group Mob is shown to be a tensor product of n hermitian holomorphic vector bundles over D. Among them, n - 1 are shown to be the line bundles and one is shown to be a rank 2 bundle. Also, each of the bundles are homogeneous with respect to Mob. The classification of irreducible homogeneous hermitian holomorphic vector bundles over D-2 of rank 3 (as well as the corresponding Cowen-Douglas class of operators) is extended to the case of D-n, n &gt; 2. It is shown that there is no irreducible n - tuple of operators in the Cowen-Douglas class B-2 (D-n) that is homogeneous with respect to Aut(D-n), n &gt; 1. Also, pairs of operators in B-3(D-2) homogeneous with respect to Aut(D-2) are produced, while it is shown that no n - tuple of operators in B-3(D-n) is homogeneous with respect to Aut(D-n), n &gt; 2.

Název v anglickém jazyce

Homogeneous Hermitian holomorphic vector bundles and operators in the Cowen-Douglas class over the poly-disc

Popis výsledku anglicky

In this article, we obtain two sets of results. The first set of results are for the case of the bi-disc while the second set of results describe in part, which of these carry over to the general case of the poly-disc. A classification of irreducible hermitian holomorphic vector bundles over D-2, homogeneous with respect to Mob x Mob, is obtained assuming that the associated representations are multiplicity-free. Among these the ones that give rise to an operator in the Cowen-Douglas class of D-2 of rank 1, 2 or 3 are determined. Any hermitian holomorphic vector bundle of rank 2 over D-n, homogeneous with respect to the n-fold direct product of the group Mob is shown to be a tensor product of n hermitian holomorphic vector bundles over D. Among them, n - 1 are shown to be the line bundles and one is shown to be a rank 2 bundle. Also, each of the bundles are homogeneous with respect to Mob. The classification of irreducible homogeneous hermitian holomorphic vector bundles over D-2 of rank 3 (as well as the corresponding Cowen-Douglas class of operators) is extended to the case of D-n, n &gt; 2. It is shown that there is no irreducible n - tuple of operators in the Cowen-Douglas class B-2 (D-n) that is homogeneous with respect to Aut(D-n), n &gt; 1. Also, pairs of operators in B-3(D-2) homogeneous with respect to Aut(D-2) are produced, while it is shown that no n - tuple of operators in B-3(D-n) is homogeneous with respect to Aut(D-n), n &gt; 2.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA21-27941S" target="_blank" >GA21-27941S: Teorie funkcí a příbuzné operátory na komplexních oblastech</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

510

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

„126031-1“-„126031-32“

Kód UT WoS článku

000821504900018

EID výsledku v databázi Scopus

2-s2.0-85123632658