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Birkhäuser

Representation Theory, Mathematical Physics, and Integrable Systems

In Honor of Nicolai Reshetikhin

  • Book
  • © 2021

Overview

Editors:
  1. Anton Alekseev

    1. Section de Mathématiques, Université de Genève, Genève 4, Switzerland

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  2. Edward Frenkel

    1. Department of Mathematics, University of California at Berkley, Berkeley, USA

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  3. Marc Rosso

    1. Mathematics Department, Institut de Mathématiques de Jussieu, Paris Cedex 13, France

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  4. Ben Webster

    1. Department of Pure Mathematics, University of Waterloo, Waterloo, Canada

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  5. Milen Yakimov

    1. Department of Mathematics, Northeastern University, Boston, USA

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  • Highlights the many significant contributions Nicolai Reshetikhin has made in mathematics and physics
  • Chapters are written by distinguished mathematicians and physicists
  • Explores the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and mathematical physics

Part of the book series: Progress in Mathematics (PM, volume 340)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Examples of Finite-Dimensional Pointed Hopf Algebras in Positive Characteristic

    • Nicolás Andruskiewitsch, Iván Angiono, István Heckenberger
    Pages 1-38

  3. Poisson Vertex Algebra Cohomology and Differential Harrison Cohomology

    • Bojko Bakalov, Alberto De Sole, Victor G. Kac, Veronica Vignoli
    Pages 39-69

  4. Theta Invariants of Lens Spaces via the BV-BFV Formalism

    • Alberto S. Cattaneo, Pavel Mnev, Konstantin Wernli
    Pages 71-110

  5. Generalized Demazure Modules and Prime Representations in Type D n

    • Vyjayanthi Chari, Justin Davis, Ryan Moruzzi Jr.
    Pages 111-134

  6. Cylindric Rhombic Tableaux and the Two-Species ASEP on a Ring

    • Sylvie Corteel, Olya Mandelshtam, Lauren Williams
    Pages 135-162

  7. Macdonald Operators and Quantum Q-Systems for Classical Types

    • Philippe Di Francesco, Rinat Kedem
    Pages 163-199

  8. The Meromorphic R-Matrix of the Yangian

    • Sachin Gautam, Valerio Toledano Laredo, Curtis Wendlandt
    Pages 201-269

  9. On Spectral Cover Equations in Simpson Integrable Systems

    • Anton A. Gerasimov, Samson L. Shatashvili
    Pages 271-281

  10. Peter-Weyl Bases, Preferred Deformations, and Schur-Weyl Duality

    • Anthony Giaquinto, Alex Gilman, Peter Tingley
    Pages 283-298

  11. Quantum Periodicity and Kirillov–Reshetikhin Modules

    • David Hernandez
    Pages 299-315

  12. A Note on the E-Polynomials of a Stratification of the Hilbert Scheme of Points

    • Yi-Ning Hsiao, Andras Szenes
    Pages 317-344

  13. Galois Action on VOA Gauge Anomalies

    • Theo Johnson-Freyd
    Pages 345-370

  14. Heisenberg-Picture Quantum Field Theory

    • Theo Johnson-Freyd
    Pages 371-409

  15. Irreducibility of the Wysiwyg Representations of Thompson’s Groups

    • Vaughan F. R. Jones
    Pages 411-430

  16. Invariants of Long Knots

    • Rinat Kashaev
    Pages 431-451

  17. Rigged Configurations and Unimodality

    • Anatol N. Kirillov
    Pages 453-496

  18. Turning Point Processes in Plane Partitions with Periodic Weights of Arbitrary Period

    • Sevak Mkrtchyan
    Pages 497-527

  19. The Skein Category of the Annulus

    • K. Al Qasimi, J. V. Stokman
    Pages 529-568

  20. Tensor Product of the Fock Representation with Its Dual and the Deligne Category

    • Vera Serganova
    Pages 569-584
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Keywords

About this book

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology.  The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements.  


Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed.


Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.



Editors and Affiliations

  • Section de Mathématiques, Université de Genève, Genève 4, Switzerland

    Anton Alekseev

  • Department of Mathematics, University of California at Berkley, Berkeley, USA

    Edward Frenkel

  • Mathematics Department, Institut de Mathématiques de Jussieu, Paris Cedex 13, France

    Marc Rosso

  • Department of Pure Mathematics, University of Waterloo, Waterloo, Canada

    Ben Webster

  • Department of Mathematics, Northeastern University, Boston, USA

    Milen Yakimov

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