Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification: In honor of Vyjayanthi Chari on the occasion of her 60th birthday

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 chapters present a broad view of the area, featuring surveys, original research, and an overview of Charis significant contributions.

Format: Paperback / softback
Length: 440 pages
Publication date: 12 March 2023
Publisher: Springer Nature Switzerland AG

This remarkable volume brings together a collection of chapters that delve into the intricate connections between representation theory and affine Lie algebras, as well as their quantum counterparts. The opening chapters, crafted from mini-courses presented during the conference "Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras, and Categorification," held in honor of Vyjayanthi Chari's 60th birthday at the Catholic University of America in Washington, D.C., in June 2018, serve as a foundational exploration of the subject. The subsequent chapters offer a comprehensive perspective on the field, encompassing surveys, original research, and a comprehensive overview of Vyjayanthi Charis's profound contributions. Written by esteemed experts in representation theory, this diverse collection addresses a wide range of topics, including:

String diagrams and categorification: These chapters provide a comprehensive introduction to the use of string diagrams in the study of quantum affine algebras and cluster algebras. They explore the interplay between these mathematical structures and various categorification techniques, shedding light on their connections and applications.

Quantum affine algebras and cluster algebras: These chapters delve into the fundamental properties and structures of quantum affine algebras and cluster algebras, exploring their symmetries, representations, and applications in mathematical physics. They provide a solid foundation for researchers seeking to understand these complex mathematical entities.

Steinberg groups for Jordan pairs: These chapters explore the role of Steinberg groups in the study of quantum affine algebras and their connections to other mathematical structures. They discuss the construction of Steinberg groups, their properties, and their applications in various areas of representation theory.

Dynamical quantum determinants and Pfaffians: These chapters explore the dynamics of quantum affine algebras and their connections to quantum mechanics. They discuss the concept of dynamical quantum determinants, their properties, and their applications in understanding the behavior of quantum systems.

Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras, and Categorification: This chapter provides an overview of the recent developments in the interactions between quantum affine algebras, cluster algebras, and other mathematical structures. It highlights the connections between these areas and their potential applications in various fields of mathematics and physics.

As a comprehensive resource for researchers in the fields of representation theory and mathematical physics, this volume offers invaluable insights and perspectives into the intricate world of affine Lie algebras and their quantum counterparts. The contributions of Vyjayanthi Charis to this field are celebrated throughout, and the chapters authored by esteemed experts provide a deep understanding of the latest developments and applications in this dynamic area of research.

Dimension: 235 x 155 (mm)
ISBN-13: 9783030638511
Edition number: 1st ed. 2021