A family of homogeneous operators in the Cowen-Douglas class over the poly-disc

@article{78326,
   author = {Deb, Prahllad and Hazra, Somnath},
   article_location = {Warsaw, Poland},
   article_number = {1},
   doi = {http://dx.doi.org/10.4064/sm220630-10-1},
   keywords = {Cowen-Douglas class; curvature; hermitian holomorphic homogeneous vector bundles; homogeneous operators},
   language = {eng},
   issn = {0039-3223},
   journal = {Studia Mathematica},
   title = {A family of homogeneous operators in the Cowen-Douglas class over the poly-disc},
   url = {https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/271/1/115001/a-family-of-homogeneous-operators-in-the-cowen-douglas-class-over-the-poly-disc},
   volume = {271},
   year = {2023}
}

TY  - JOUR
ID  - 78326
AU  - Deb, Prahllad - Hazra, Somnath
PY  - 2023
TI  - A family of homogeneous operators in the Cowen-Douglas class over the poly-disc
JF  - Studia Mathematica
VL  - 271
IS  - 1
SP  - 65-84
EP  - 65-84
PB  - IMPAN - Institute of Mathematics. Polish Academy of Sciences
SN  - 00393223
KW  - Cowen-Douglas class
KW  - curvature
KW  - hermitian holomorphic homogeneous vector bundles
KW  - homogeneous operators
UR  - https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/271/1/115001/a-family-of-homogeneous-operators-in-the-cowen-douglas-class-over-the-poly-disc
N2  - We construct a large family of positive definite kernels K : Dn x Dn-+ M(r, C), holomorphic in the first variable and anti-holomorphic in the second, that are quasi-invariant with respect to the subgroup Mob x center dot center dot center dot x Mob (n times) of the bi-holomorphic automorphism group of Dn. The adjoint of the n-tuple of the multiplication operators by the co-ordinate functions is then homogeneous with respect to this subgroup on the Hilbert space ?-lK determined by K. We show that these n-tuples are irreducible, are in the Cowen-Douglas class Br(Dn) and are mutually pairwise unitarily inequivalent.
ER  - 

DEB, Prahllad and Somnath HAZRA. A family of homogeneous operators in the Cowen-Douglas class over the poly-disc. \textit{Studia Mathematica}. Warsaw, Poland: IMPAN - Institute of Mathematics. Polish Academy of Sciences, 2023, vol.~271, No~1, p.~65-84. ISSN~0039-3223. Available from: https://dx.doi.org/10.4064/sm220630-10-1.