J 2022

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

DEB, Prahllad a Somnath HAZRA

Základní údaje

Originální název

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

Autoři

DEB, Prahllad (356 Indie) a Somnath HAZRA (356 Indie, garant, domácí)

Vydání

Journal of Mathematical Analysis and Applications, San Diego (USA), Academic Press Inc. Elsevier Science, 2022, 0022-247X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Kód RIV

RIV/47813059:19610/22:A0000110

Organizační jednotka

Matematický ústav v Opavě

UT WoS

000821504900018

Klíčová slova anglicky

Cowen-Douglas class; Homogeneous operators; Hermitian holomorphic homogeneous vector bundles; Curvature; Representation; Lie algebra

Štítky

Příznaky

Mezinárodní význam, Recenzováno

Návaznosti

GA21-27941S, projekt VaV.
Změněno: 1. 3. 2023 15:15, Mgr. Aleš Ryšavý

Anotace

V originále

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 > 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 > 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 > 2.