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Conformal Symmetry Breaking Differential Operators On Differential Forms

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Conformal Symmetry Breaking Differential Operators On Differential Forms

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Author : Matthias Fischmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18

Conformal Symmetry Breaking Differential Operators On Differential Forms written by Matthias Fischmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Education categories.

We study conformal symmetry breaking diﬀerential operators which map dif-ferential 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 mod-ules 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 re-lated 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 opera- tors 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.

Conformal Symmetry Breaking Operators For Differential Forms On Spheres

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Author : Toshiyuki Kobayashi
language : en
Publisher: Springer
Release Date : 2016-10-11

Conformal Symmetry Breaking Operators For Differential Forms On Spheres written by Toshiyuki Kobayashi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-11 with Mathematics categories.

This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin–Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valued factorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is a general method to construct intertwining operators between C∞-induced representations or to find singular vectors of Verma modules in the context of branching rules, as solutions to differential equations on the Fourier transform side. The book gives a new extension of the F-method to the matrix-valued case in the general setting, which could be applied to other problems as well. This book offers a self-contained introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in differential geometry, representation theory, and theoretical physics.

Symmetry In Geometry And Analysis Volume 2

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Author : Michael Pevzner
language : en
Publisher: Springer Nature
Release Date : 2025-02-10

Symmetry In Geometry And Analysis Volume 2 written by Michael Pevzner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-10 with Mathematics categories.

Symmetry In Geometry And Analysis Volume 1

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Author : Michael Pevzner
language : en
Publisher: Springer Nature
Release Date : 2025-02-09

Symmetry In Geometry And Analysis Volume 1 written by Michael Pevzner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-09 with Mathematics categories.

Symmetry in Geometry and Analysis is a Festschrift honoring Toshiyuki Kobayashi. The three volumes feature 35 selected contributions from invited speakers of twin conferences held in June 2022 in Reims, France, and in September 2022 in Tokyo, Japan. These contributions highlight the profound impact of Prof. Kobayashi’s pioneering ideas, groundbreaking discoveries, and significant achievements in the development of analytic representation theory, noncommutative harmonic analysis, and the geometry of discontinuous groups beyond the Riemannian context, among other areas, over the past four decades. The first volume of the Festschrift includes a survey article on Kobayashi’s innovative contributions to Mathematics, emphasizing their influence and introducing new perspectives across various fields. Original articles contained in Volume 1 focus on differential geometry with symmetries as well as algebraic and geometric aspects of representation theory of reductive Lie groups and related topics. Contributions are by Velleda Baldoni, Dan Barbasch, Leticia Barchini, Sigiswald Barbier, Yves Benoist, Sam Claerebout, Michael Eastwood, Wee Teck Gan, William M. Goldman, Roger Howe, Kazuki Kannaka, Toshihisa Kubo, Hung Yean Loke, Jia-Jun Ma, Reiko Miyaoka, Kento Ogawa, Takayuki Okuda, Yoshiki Oshima, Paul-Émile Paradan, Annegret Paul, Michael Pevzner, Yiannis Sakellaridis, Atsumi Sasaki, Gordan Savin, Hideko Sekiguchi, Binyong Sun, Yuichiro Tanaka, Koichi Tojo, Peter Trapa, Michèle Vergne, Joseph A. Wolf, Kayue Daniel Wong, and Chen-Bo Zhu. The Mathematical Work of Toshiyuki Kobayashi is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Asymptotic Counting In Conformal Dynamical Systems

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Author : Mark Pollicott
language : en
Publisher: American Mathematical Society
Release Date : 2021-09-24

Asymptotic Counting In Conformal Dynamical Systems written by Mark Pollicott and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-24 with Mathematics categories.

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Representation Theory And Harmonic Analysis On Symmetric Spaces

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Author : Jens Gerlach Christensen
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-27

Representation Theory And Harmonic Analysis On Symmetric Spaces written by Jens Gerlach Christensen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-27 with Mathematics categories.

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis, in honor of Gestur Ólafsson's 65th birthday, held on January 4, 2017, in Atlanta, Georgia. The articles in this volume provide fresh perspectives on many different directions within harmonic analysis, highlighting the connections between harmonic analysis and the areas of integral geometry, complex analysis, operator algebras, Lie algebras, special functions, and differential operators. The breadth of contributions highlights the diversity of current research in harmonic analysis and shows that it continues to be a vibrant and fruitful field of inquiry.

Space Time Matter

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Author : Jochen Brüning
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-04-09

Space Time Matter written by Jochen Brüning and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-09 with Mathematics categories.

This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

Hamiltonian Perturbation Theory For Ultra Differentiable Functions

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Author : Abed Bounemoura
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21

Hamiltonian Perturbation Theory For Ultra Differentiable Functions written by Abed Bounemoura and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Education categories.

Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means of hard implicit function theorems. They comprise Gevrey functions and thus, as a limiting case, analytic functions. Using majorizing series, we manage to characterize them in terms of a real sequence M bounding the growth of derivatives. In this functional setting, we prove two fundamental results of Hamiltonian perturbation theory: the invariant torus theorem, where the invariant torus remains ultra-differentiable under the assumption that its frequency satisfies some arithmetic condition which we call BRM, and which generalizes the Bruno-R¨ussmann condition; and Nekhoroshev’s theorem, where the stability time depends on the ultra-differentiable class of the pertubation, through the same sequence M. Our proof uses periodic averaging, while a substitute for the analyticity width allows us to bypass analytic smoothing. We also prove converse statements on the destruction of invariant tori and on the existence of diffusing orbits with ultra-differentiable perturbations, by respectively mimicking a construction of Bessi (in the analytic category) and MarcoSauzin (in the Gevrey non-analytic category). When the perturbation space satisfies some additional condition (we then call it matching), we manage to narrow the gap between stability hypotheses (e.g. the BRM condition) and instability hypotheses, thus circumbscribing the stability threshold. The formulas relating the growth M of derivatives of the perturbation on the one hand, and the arithmetics of robust frequencies or the stability time on the other hand, bring light to the competition between stability properties of nearly integrable systems and the distance to integrability. Due to our method of proof using width of regularity as a regularizing parameter, these formulas are closer to optimal as the the regularity tends to analyticity

Instability Index Theorem And Exponential Trichotomy For Linear Hamiltonian Pdes

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Author : Zhiwu Lin
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-02

Instability Index Theorem And Exponential Trichotomy For Linear Hamiltonian Pdes written by Zhiwu Lin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-02 with Mathematics categories.

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Geometric Methods In Physics Xxxv

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Author : Piotr Kielanowski
language : en
Publisher: Birkhäuser
Release Date : 2018-02-10

Geometric Methods In Physics Xxxv written by Piotr Kielanowski and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-10 with Mathematics categories.

This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.

Conformal Symmetry Breaking Differential Operators On Differential Forms

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