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  • 1
    Online Resource
    Online Resource
    Branes and DAHA Representations. (2023)
    Cham :Springer,
    Details
    UID:
    almahu_9949568765502882
    Format: 1 online resource (147 pages)
    Edition: 1st ed.
    ISBN: 9783031281549
    Series Statement: SpringerBriefs in Mathematical Physics Series ; v.48
    Note: Intro -- Contents -- 1 Introduction -- 1.1 Background -- 1.2 Results -- 1.3 Structure -- 2 2d Sigma-Models and DAHA -- 2.1 Higgs Bundles and Flat Connections -- 2.2 DAHA of Rank One and Its Spherical Algebra -- 2.3 Canonical Coisotropic Branes in A-models -- 2.3.1 Spherical DAHA as the Algebra of (mathfrakBcc,mathfrakBcc)-Strings -- 2.4 Lagrangian A-Branes and Modules of mathscrOq(mathfrakX) -- 2.5 (A,B,A)-Branes for Polynomial Representations -- 2.6 Branes with Compact Supports and Finite-Dimensional Representations: Object Matching -- 2.6.1 Generic Fibers of the Hitchin Fibration -- 2.6.2 Irreducible Components in Singular Fibers of Type I2 -- 2.6.3 Moduli Space of G-Bundles -- 2.6.4 Exceptional Divisors -- 2.7 Bound States of Branes and Short Exact Sequences: Morphism Matching -- 2.7.1 At Singular Fiber of Type I2 -- 2.7.2 At Global Nilpotent Cone of Type I0* -- 3 3d Theories and Modularity -- 3.1 DAHA and Modularity -- 3.1.1 SU(2): Refined Chern-Simons and TQFT Associated to Argyres-Douglas Theory -- 3.1.2 SU(N): Higher Rank Generalization -- 3.2 Relation to Skein Modules and MTC[M3] -- 4 4d Theories, Fivebranes, and M-Theory -- 4.1 Coulomb Branches of 4d N=2* Theories of Rank One -- 4.2 Algebra of Line Operators -- 4.3 Including Surface Operator -- Appendix A Glossary of Symbols -- Appendix B Basics of DAHA -- B.1 DAHA -- B.1.1 Double Affine Braid Group and Double Affine Weyl Group -- B.1.2 PBW Theorem for DAHA -- B.1.3 Spherical Subalgebra -- B.1.4 Braid Group and SL(2,mathbbZ) Action -- B.1.5 Polynomial Representation of DAHA -- B.1.6 Symmetric Bilinear Form -- B.1.7 Degenerations -- B.2 DAHA of Type A1 -- B.2.1 Polynomial Representation -- B.2.2 Functional Representation -- B.2.3 Trigonometric Cherednik Algebra of Type A1 -- B.2.4 Rational Cherednik Algebra of Type A1 -- Appendix C Quantum Torus Algebra. , C.1 Representations of Quantum Torus Algebra -- C.1.1 Unitary Representations -- C.1.2 Non-unitary Representations -- C.1.3 Geometric Viewpoint -- C.2 Branes for Quantum Torus Algebra -- C.2.1 Cyclic Representations -- C.2.2 Polynomial Representations -- C.3 Symmetrized Quantum Torus -- C.3.1 Representation Theory -- C.3.2 Corresponding Branes -- Appendix D 3d mathcalN=4 Theories and Cherednik Algebras -- D.1 Coulomb Branches of 3d mathcalN=4 Theories -- D.2 3d mathcalN=4 Coulomb Branches and Cherednik Algebras -- Appendix References.
    Additional Edition: Print version: Gukov, Sergei Branes and DAHA Representations Cham : Springer,c2023 ISBN 9783031281532
    Language: English
    Keywords: Electronic books. ; Electronic books.
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  • 2
    Online Resource
    Online Resource
    Branes and DAHA Representations (2023)
    Cham :Springer Nature Switzerland :
    Details
    UID:
    almahu_9949561319302882
    Format: 1 online resource (147 pages)
    Edition: 1st ed. 2023.
    ISBN: 3-031-28154-3
    Series Statement: SpringerBriefs in Mathematical Physics, 48
    Content: In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which comes from string theory, is explored in the book. This open access book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules. The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction. The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory. This is an open access book.
    Note: Introduction -- 2d sigma-models and DAHA -- 3d theories and modularity.-4 d theories, fivebranes, and M-theory -- Appendix.
    Additional Edition: ISBN 3-031-28153-5
    Language: English
    DOI: 10.1007/978-3-031-28154-9
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  • 3
    Online Resource
    Online Resource
    Branes and DAHA Representations (2023)
    Cham : Springer Nature
    Details
    UID:
    gbv_1877797332
    Format: 1 Online-Ressource (143 p.)
    ISBN: 9783031281549 , 9783031281532
    Series Statement: SpringerBriefs in Mathematical Physics
    Content: In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which comes from string theory, is explored in the book. This open access book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules. The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction. The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory. This is an open access book
    Note: English
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    URL: kostenfrei
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  • 4
    Online Resource
    Online Resource
    Branes and DAHA Representations (2023)
    Cham :Springer Nature Switzerland :
    Details
    UID:
    almahu_9949552710402882
    Format: VI, 143 p. 42 illus., 25 illus. in color. , online resource.
    Edition: 1st ed. 2023.
    ISBN: 9783031281549
    Series Statement: SpringerBriefs in Mathematical Physics, 48
    Content: In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which comes from string theory, is explored in the book. This open access book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules. The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction. The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory. This is an open access book.
    Note: Introduction -- 2d sigma-models and DAHA -- 3d theories and modularity.-4 d theories, fivebranes, and M-theory -- Appendix.
    In: Springer Nature eBook
    Additional Edition: Printed edition: ISBN 9783031281532
    Additional Edition: Printed edition: ISBN 9783031281556
    Language: English
    DOI: 10.1007/978-3-031-28154-9
    URL: https://doi.org/10.1007/978-3-031-28154-9
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  • 5
    Online Resource
    Online Resource
    Branes and DAHA Representations (2023)
    Cham :Springer Nature Switzerland :
    Details
    UID:
    edocfu_9961235410202883
    Format: 1 online resource (147 pages)
    Edition: 1st ed. 2023.
    ISBN: 3-031-28154-3
    Series Statement: SpringerBriefs in Mathematical Physics, 48
    Content: In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which comes from string theory, is explored in the book. This open access book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules. The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction. The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory. This is an open access book.
    Note: Introduction -- 2d sigma-models and DAHA -- 3d theories and modularity.-4 d theories, fivebranes, and M-theory -- Appendix.
    Additional Edition: ISBN 3-031-28153-5
    Language: English
    DOI: 10.1007/978-3-031-28154-9
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Open Access Request
    FU Berlin
  • 6
    Online Resource
    Online Resource
    Branes and DAHA Representations (2023)
    Cham :Springer Nature Switzerland :
    Details
    UID:
    edoccha_9961235410202883
    Format: 1 online resource (147 pages)
    Edition: 1st ed. 2023.
    ISBN: 3-031-28154-3
    Series Statement: SpringerBriefs in Mathematical Physics, 48
    Content: In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which comes from string theory, is explored in the book. This open access book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules. The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction. The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory. This is an open access book.
    Note: Introduction -- 2d sigma-models and DAHA -- 3d theories and modularity.-4 d theories, fivebranes, and M-theory -- Appendix.
    Additional Edition: ISBN 3-031-28153-5
    Language: English
    DOI: 10.1007/978-3-031-28154-9
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Online Resource
    Open Access Request
    Charité
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