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Representations and Nilpotent Orbits of Lie Algebraic Systems

In Honour of the 75th Birthday of Tony Joseph

  • Book
  • © 2019

Overview

Editors:
  1. Maria Gorelik

    1. Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel

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  2. Vladimir Hinich

    1. Department of Mathematics, University of Haifa, Haifa, Israel

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    You can also search for this editor in PubMed   Google Scholar

  3. Anna Melnikov

    1. Department of Mathematics, University of Haifa, Haifa, Israel

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  • Commemorates the mathematical achievements of Anthony Joseph, one of Lie theory’s leading figures
  • Explores recent advances in topics that Joseph fundamentally influenced
  • Equips readers with an understanding of various subjects within Lie algebra and representation theory

Part of the book series: Progress in Mathematics (PM, volume 330)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Singular Support of a Vertex Algebra and the Arc Space of Its Associated Scheme

    • Tomoyuki Arakawa, Andrew R. Linshaw
    Pages 1-17

  3. On Cacti and Crystals

    • Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
    Pages 19-72

  4. Quotients for Sheets of Conjugacy Classes

    • Giovanna Carnovale, Francesco Esposito
    Pages 73-90

  5. About Polynomiality of the Poisson Semicentre for Parabolic Subalgebras

    • Florence Fauquant-Millet
    Pages 91-110

  6. On Dynkin Gradings in Simple Lie Algebras

    • Alexander Elashvili, Mamuka Jibladze, Victor Kac
    Pages 111-131

  7. Multiplicative Slices, Relativistic Toda and Shifted Quantum Affine Algebras

    • Michael Finkelberg, Alexander Tsymbaliuk
    Pages 133-304

  8. Some Properties of Orbital Varieties in Extremal Nilpotent Orbits

    • Lucas Fresse
    Pages 305-329

  9. On Involutions in the Weyl Group and B-Orbit Closures in the Orthogonal Case

    • Mikhail V. Ignatyev
    Pages 331-355

  10. Proper Self-Similar Triangle Tiling and Representing Weight Diagrams in the Plane

    • Anthony Joseph
    Pages 357-409

  11. Closures of On-Orbits in the Flag Variety for GLn

    • William M. McGovern
    Pages 411-419

  12. The Spin Calogero-Sutherland Model at Infinity

    • Maxim Nazarov
    Pages 421-439

  13. Semi-Direct Products Involving Sp2n or Spinn with Free Algebras of Symmetric Invariants

    • Dmitri I. Panyushev, Oksana S. Yakimova
    Pages 441-470

  14. Primitive Ideals of \({\mathrm {U}}(\mathfrak {sl}(\infty ))\) and the Robinson–Schensted Algorithm at Infinity

    • Ivan Penkov, Alexey Petukhov
    Pages 471-499

  15. Prime Spectra of Abelian 2-Categories and Categorifications of Richardson Varieties

    • Kent Vashaw, Milen Yakimov
    Pages 501-553
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Keywords

About this book

This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including:
  • Primitive ideals
  • Invariant theory
  • Geometry of Lie group actions
  • Quantum affine algebras
  • Yangians
  • Categorification
  • Vertex algebras

This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Editors and Affiliations

  • Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel

    Maria Gorelik

  • Department of Mathematics, University of Haifa, Haifa, Israel

    Vladimir Hinich, Anna Melnikov

Bibliographic Information

  • Book Title: Representations and Nilpotent Orbits of Lie Algebraic Systems

  • Book Subtitle: In Honour of the 75th Birthday of Tony Joseph

  • Editors: Maria Gorelik, Vladimir Hinich, Anna Melnikov

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-23531-4

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-23530-7Published: 05 November 2019

  • Softcover ISBN: 978-3-030-23533-8Published: 05 November 2020

  • eBook ISBN: 978-3-030-23531-4Published: 18 October 2019

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XVII, 553

  • Number of Illustrations: 59 b/w illustrations, 16 illustrations in colour

  • Topics: Topological Groups, Lie Groups

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