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Double Affine Hecke Algebras And Congruence Groups
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Book Synopsis DOUBLE AFFINE HECKE ALGEBRAS AND CONGRUENCE GROUPS. by : BOGDAN. SAHI ION (SIDDHARTHA.)
Download or read book DOUBLE AFFINE HECKE ALGEBRAS AND CONGRUENCE GROUPS. written by BOGDAN. SAHI ION (SIDDHARTHA.) and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Double Affine Hecke Algebras and Congruence Groups by : Bogdan Ion
Download or read book Double Affine Hecke Algebras and Congruence Groups written by Bogdan Ion and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/DAHA always admit a faithful action by auto-morphisms of a finite index subgroup of the Artin group of type A2, which descends to a faithful outer action of a congruence subgroup of SL(2, Z)or PSL(2, Z). This was previously known only in some special cases and, to the best of our knowledge, not even conjectured to hold in full generality. It turns out that the structural intricacies of DAAG/DAHA are captured by the underlying semisimple data and, to a large extent, even by adjoint data; we prove our main result by reduction to the adjoint case. Adjoint DAAG/DAHA correspond in a natural way to affine Lie algebras, or more precisely to their affinized Weyl groups, which are the semi-direct products W Q∨ of the Weyl group W with the coroot lattice Q∨. They were defined topologically by van der Lek, and independently, algebraically, by Cherednik. We now describe our results for the adjoint case in greater detail. We first give a new Coxeter-type presentation for adjoint DAAG as quotients of the Coxeter braid groups associated to certain crystallographic diagrams that we call double affine Coxeter diagrams. As a consequence we show that the rank two Artin groups of type A2,B2,G2 act by automorphisms on the adjoint DAAG/DAHA associated to affine Lie algebras of twist number r =1, 2, 3, respec-tively. This extends a fundamental result of Cherednik for r =1. We show further that the above rank two Artin group action descends to an outer action of the congruence subgroup Γ1(r). In particular, Γ1(r) acts naturally on the set of isomorphism classes of representations of an adjoint DAAG/DAHA of twist number r, giving rise to a projective representation of Γ1(r)on the spaceof aΓ1(r)-stable representation. We also provide a classification of the involutions of Kazhdan-Lusztig type that appear in the context of these actions.
Book Synopsis Double Affine Hecke Algebras by : Ivan Cherednik
Download or read book Double Affine Hecke Algebras written by Ivan Cherednik and published by Cambridge University Press. This book was released on 2005-03-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an essentially self-contained monograph in an intriguing field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications. Chapter 1 is devoted to the Knizhnik-Zamolodchikov equations attached to root systems and their relations to affine Hecke algebras, Kac-Moody algebras, and Fourier analysis. Chapter 2 contains a systematic exposition of the representation theory of the one-dimensional DAHA. It is the simplest case but far from trivial with deep connections in the theory of special functions. Chapter 3 is about DAHA in full generality, including applications to Macdonald polynomials, Fourier transforms, Gauss-Selberg integrals, Verlinde algebras, and Gaussian sums. This book is designed for mathematicians and physicists, experts and students, for those who want to master the double Hecke algebra technique. Visit http://arxiv.org/math.QA/0404307 to read Chapter 0 and selected topics from other chapters.
Book Synopsis Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions by : Tom H. Koornwinder
Download or read book Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions written by Tom H. Koornwinder and published by Cambridge University Press. This book was released on 2020-10-15 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.
Book Synopsis Eisenstein Series and Automorphic Representations by : Philipp Fleig
Download or read book Eisenstein Series and Automorphic Representations written by Philipp Fleig and published by Cambridge Studies in Advanced. This book was released on 2018-07-05 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Book Synopsis Intense Automorphisms of Finite Groups by : Mima Stanojkovski
Download or read book Intense Automorphisms of Finite Groups written by Mima Stanojkovski and published by American Mathematical Society. This book was released on 2021-12-09 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Naturality and Mapping Class Groups in Heegard Floer Homology by : András Juhász
Download or read book Naturality and Mapping Class Groups in Heegard Floer Homology written by András Juhász and published by American Mathematical Society. This book was released on 2021-12-09 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Non-Kissing Complexes and Tau-Tilting for Gentle Algebras by : Yann Palu
Download or read book Non-Kissing Complexes and Tau-Tilting for Gentle Algebras written by Yann Palu and published by American Mathematical Society. This book was released on 2021-12-30 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry by : Stuart Margolis
Download or read book Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry written by Stuart Margolis and published by American Mathematical Society. This book was released on 2021-12-30 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function by : Athanassios S. Fokas
Download or read book On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function written by Athanassios S. Fokas and published by American Mathematical Society. This book was released on 2022-02-02 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities by : William Gignac
Download or read book Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities written by William Gignac and published by American Mathematical Society. This book was released on 2021-11-16 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Goodwillie Approximations to Higher Categories by : Gijs Heuts
Download or read book Goodwillie Approximations to Higher Categories written by Gijs Heuts and published by American Mathematical Society. This book was released on 2021-11-16 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Hamiltonian Perturbation Theory for Ultra-Differentiable Functions by : Abed Bounemoura
Download or read book Hamiltonian Perturbation Theory for Ultra-Differentiable Functions written by Abed Bounemoura and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Hardy-Littlewood and Ulyanov Inequalities by : Yurii Kolomoitsev
Download or read book Hardy-Littlewood and Ulyanov Inequalities written by Yurii Kolomoitsev and published by American Mathematical Society. This book was released on 2021-09-24 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Noncommutative Homological Mirror Functor by : Cheol-Hyun Cho
Download or read book Noncommutative Homological Mirror Functor written by Cheol-Hyun Cho and published by American Mathematical Society. This book was released on 2021-09-24 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Asymptotic Counting in Conformal Dynamical Systems by : Mark Pollicott
Download or read book Asymptotic Counting in Conformal Dynamical Systems written by Mark Pollicott and published by American Mathematical Society. This book was released on 2021-09-24 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups by : Pierre Patie
Download or read book Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups written by Pierre Patie and published by American Mathematical Society. This book was released on 2021-11-16 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.