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

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

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.

• Vyjayanthi Chari representation theory
• Vyjayanthi Chari quantum algebra
• Quantum affine algebras
• Quantum affine algebras representation
• Quantum groups
• Monoidal categories
• Categorification representation
• Cluster algebras
• String diagrams
• Steinberg groups
• Hecke algebra p-adic field
• Weyl group Cartan matrix
• Kashiwara functions
• Lusztig crystals
• Dynamical quantum groups

• 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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