Branes and DAHA Representations.

By: Gukov, SergeiContributor(s): Koroteev, Peter | Nawata, Satoshi | Pei, Du | Saberi, IngmarMaterial type: TextTextSeries: SpringerBriefs in Mathematical Physics SeriesPublisher: Cham : Springer, 2023Copyright date: �2023Edition: 1st edDescription: 1 online resource (147 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783031281549Genre/Form: Electronic books.Additional physical formats: Print version:: Branes and DAHA RepresentationsLOC classification: QC19.2-20.85Online resources: Click to View
Contents:
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.
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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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2023. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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