Complex manifolds and unitary representations

1971 ◽  
pp. 242-287
Author(s):  
Joseph A. Wolf
Keyword(s):  
Unitary Representations ◽  
Complex Manifolds

A characterization of complex manifolds biholomorphic to a circular domain

1985 ◽  
Vol 189 (3) ◽  
pp. 343-363 ◽  
Author(s):  
Giorgio Patrizio
Keyword(s):  
Circular Domain ◽  
Complex Manifolds

scholarly journals Defect CFT techniques in the 6d $$ \mathcal{N} $$ = (2, 0) theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nadav Drukker ◽  
Malte Probst ◽  
Maxime Trépanier
Keyword(s):  
Stress Tensor ◽  
Unitary Representations ◽  
Point Function ◽  
Displacement Operator ◽  
Expectation Value ◽  
Operator Expansion ◽  
Bulk Stress ◽  
Defect Operator ◽  
Tensor Multiplet

Abstract Surface operators are among the most important observables of the 6d $$ \mathcal{N} $$ N = (2, 0) theory. Here we apply the tools of defect CFT to study local operator insertions into the 1/2-BPS plane. We first relate the 2-point function of the displacement operator to the expectation value of the bulk stress tensor and translate this relation into a constraint on the anomaly coefficients associated with the defect. Secondly, we study the defect operator expansion of the stress tensor multiplet and identify several new operators of the defect CFT. Technical results derived along the way include the explicit supersymmetry tranformations of the stress tensor multiplet and the classification of unitary representations of the superconformal algebra preserved by the defect.

scholarly journals On contact structures of real and complex manifolds

1963 ◽  
Vol 15 (3) ◽  
pp. 227-252 ◽  
Author(s):  
Seizi Takizawa
Keyword(s):  
Contact Structures ◽  
Complex Manifolds

scholarly journals Schottky groups acting on homogeneous rational manifolds

2019 ◽  
Vol 2019 (753) ◽  
pp. 23-56 ◽  
Author(s):  
Christian Miebach ◽  
Karl Oeljeklaus
Keyword(s):  
Deformation Theory ◽  
Group Actions ◽  
Picard Group ◽  
Schottky Group ◽  
Fundamental Groups ◽  
Complex Manifolds ◽  
Schottky Groups ◽  
Algebraic Dimension ◽  
Geometric Invariants ◽  
Compact Complex Manifolds

AbstractWe systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori’s well-known construction. This yields new examples of non-Kähler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to Lárusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of {{\rm{SL}}(2,\mathbb{C})/\Gamma} for Γ a discrete free loxodromic subgroup of {{\rm{SL}}(2,\mathbb{C})}, previously obtained by A. Guillot.

scholarly journals Higher-page Bott–Chern and Aeppli cohomologies and applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dan Popovici ◽  
Jonas Stelzig ◽  
Luis Ugarte
Keyword(s):  
Positive Integer ◽  
Spectral Sequence ◽  
Complex Manifolds ◽  
Serre Duality ◽  
Frölicher Spectral Sequence ◽  
Compact Complex Manifolds

Abstract For every positive integer r, we introduce two new cohomologies, that we call E r {E_{r}} -Bott–Chern and E r {E_{r}} -Aeppli, on compact complex manifolds. When r = 1 {r\kern-1.0pt=\kern-1.0pt1} , they coincide with the usual Bott–Chern and Aeppli cohomologies, but they are coarser, respectively finer, than these when r ≥ 2 {r\geq 2} . They provide analogues in the Bott–Chern–Aeppli context of the E r {E_{r}} -cohomologies featuring in the Frölicher spectral sequence of the manifold. We apply these new cohomologies in several ways to characterise the notion of page- ( r - 1 ) {(r-1)} - ∂ ⁡ ∂ ¯ {\partial\bar{\partial}} -manifolds that we introduced very recently. We also prove analogues of the Serre duality for these higher-page Bott–Chern and Aeppli cohomologies and for the spaces featuring in the Frölicher spectral sequence. We obtain a further group of applications of our cohomologies to the study of Hermitian-symplectic and strongly Gauduchon metrics for which we show that they provide the natural cohomological framework.

scholarly journals Heisenberg–Weyl Groups and Generalized Hermite Functions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1060
Author(s):  
Enrico Celeghini ◽  
Manuel Gadella ◽  
Mariano A. del del Olmo
Keyword(s):  
Hilbert Space ◽  
Fourier Transform ◽  
Heisenberg Group ◽  
Real Line ◽  
Hermite Functions ◽  
Unitary Representations ◽  
Weyl Groups ◽  
The Real ◽  
Symmetry Properties ◽  
The Fourier Transform

We introduce a multi-parameter family of bases in the Hilbert space L2(R) that are associated to a set of Hermite functions, which also serve as a basis for L2(R). The Hermite functions are eigenfunctions of the Fourier transform, a property that is, in some sense, shared by these “generalized Hermite functions”. The construction of these new bases is grounded on some symmetry properties of the real line under translations, dilations and reflexions as well as certain properties of the Fourier transform. We show how these generalized Hermite functions are transformed under the unitary representations of a series of groups, including the Weyl–Heisenberg group and some of their extensions.

scholarly journals Universality and scaling of correlations between zeros on complex manifolds

2000 ◽  
Vol 142 (2) ◽  
pp. 351-395 ◽  
Author(s):  
Pavel Bleher ◽  
Bernard Shiffman ◽  
Steve Zelditch
Keyword(s):  
Complex Manifolds ◽  
Correlations Between Zeros
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