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Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification

In honor of Vyjayanthi Chari on the occasion of her 60th birthday

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  • © 2021

Overview

Editors:
  1. Jacob Greenstein

    1. Department of Mathematics, University of California, Riverside, Riverside, USA

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  2. David Hernandez

    1. IMJ-PRG, Université de Paris, Paris, France

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  3. Kailash C. Misra

    1. Department of Mathematics, North Carolina State University, Raleigh, USA

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  4. Prasad Senesi

    1. Department of Mathematics, Catholic University of America, Washington D.C., USA

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  • Examines representation theory as connected with affine Lie algebras and their quantum analogues
  • Presents a broad view of the area, including mini-courses, surveys, and original research
  • Celebrates the significant impact Vyjayanthi Chari has had on this area of research

Part of the book series: Progress in Mathematics (PM, volume 337)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxiv
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  2. Courses

    1. Front Matter

      Pages 1-1
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    2. String Diagrams and Categorification

      • Alistair Savage
      Pages 3-36

    3. Quantum Affine Algebras and Cluster Algebras

      • David Hernandez, Bernard Leclerc
      Pages 37-65

  3. Surveys

    1. Front Matter

      Pages 67-67
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    2. Work of Vyjayanthi Chari

      • Jacob Greenstein, David Hernandez
      Pages 69-75

    3. Steinberg Groups for Jordan Pairs: An Introduction with Open Problems

      • Erhard Neher
      Pages 77-114

    4. On the Hecke-Algebraic Approach for General Linear Groups Over a p-Adic Field

      • Maxim Gurevich
      Pages 115-144

  4. Papers

    1. Front Matter

      Pages 145-145
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    2. Categorical Representations and Classical p-Adic Groups

      • Michela Varagnolo, Eric Vasserot
      Pages 147-179

    3. Formulae of ı-Divided Powers in \({\mathbf {U}}_q(\mathfrak {sl}_2)\), II

      • Weiqiang Wang, Collin Berman
      Pages 181-243

    4. Longest Weyl Group Elements in Action

      • Yiqiang Li, Yan Ling
      Pages 245-276

    5. Dual Kashiwara Functions for the B(∞) Crystal in the Bipartite Case

      • Anthony Joseph
      Pages 277-322

    6. Lusztig’s t-Analogue of Weight Multiplicity via Crystals

      • Cédric Lecouvey, Cristian Lenart
      Pages 323-357

    7. Conormal Varieties on the Cominuscule Grassmannian

      • V. Lakshmibai, Rahul Singh
      Pages 359-392

    8. Evaluation Modules for Quantum Toroidal \(\mathfrak {gl}_n\) Algebras

      • Boris Feigin, Michio Jimbo, Evgeny Mukhin
      Pages 393-425

    9. Dynamical Quantum Determinants and Pfaffians

      • Naihuan Jing, Jian Zhang
      Pages 427-440
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Keywords

About this book

This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including:
  • String diagrams and categorification
  • Quantum affine algebras and cluster algebras
  • Steinberg groups for Jordan pairs
  • Dynamical quantum determinants and Pfaffians

Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.

Editors and Affiliations

  • Department of Mathematics, University of California, Riverside, Riverside, USA

    Jacob Greenstein

  • IMJ-PRG, Université de Paris, Paris, France

    David Hernandez

  • Department of Mathematics, North Carolina State University, Raleigh, USA

    Kailash C. Misra

  • Department of Mathematics, Catholic University of America, Washington D.C., USA

    Prasad Senesi

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