Shuffle Approach Towards Quantum Affine and Toroidal Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Shuffle Approach Towards Quantum Affine and Toroidal Algebras write by Alexander Tsymbaliuk. This book was released on 2023-08-07. Shuffle Approach Towards Quantum Affine and Toroidal Algebras available in PDF, EPUB and Kindle. This book is based on the author's mini course delivered at Tokyo University of Marine Science and Technology in March 2019. The shuffle approach to Drinfeld–Jimbo quantum groups of finite type (embedding their "positive" subalgebras into q-deformed shuffle algebras) was first developed independently in the 1990s by J. Green, M. Rosso, and P. Schauenburg. Motivated by similar ideas, B. Feigin and A. Odesskii proposed a shuffle approach to elliptic quantum groups around the same time. The shuffle algebras in the present book can be viewed as trigonometric degenerations of the Feigin–Odesskii elliptic shuffle algebras. They provide combinatorial models for the "positive" subalgebras of quantum affine algebras in their loop realizations. These algebras appeared first in that context in the work of B. Enriquez. Over the last decade, the shuffle approach has been applied to various problems in combinatorics (combinatorics of Macdonald polynomials and Dyck paths, generalization to wreath Macdonald polynomials and operators), geometric representation theory (especially the study of quantum algebras’ actions on the equivariant K-theories of various moduli spaces such as affine Laumon spaces, Nakajima quiver varieties, nested Hilbert schemes), and mathematical physics (the Bethe ansatz, quantum Q-systems, and quantized Coulomb branches of quiver gauge theories, to name just a few). While this area is still under active investigation, the present book focuses on quantum affine/toroidal algebras of type A and their shuffle realization, which have already illustrated a broad spectrum of techniques. The basic results and structures discussed in the book are of crucial importance for studying intrinsic properties of quantum affinized algebras and are instrumental to the aforementioned applications.
Shuffle Approach Towards Quantum Affine and Toroidal Algebras: Quantum toroidal sln, its representations, and Bethe subalgebras
Shuffle Approach Towards Quantum Affine and Toroidal Algebras: Quantum toroidal sln, its representations, and Bethe subalgebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Shuffle Approach Towards Quantum Affine and Toroidal Algebras: Quantum toroidal sln, its representations, and Bethe subalgebras write by Alexander Tsymbaliuk. This book was released on 2023. Shuffle Approach Towards Quantum Affine and Toroidal Algebras: Quantum toroidal sln, its representations, and Bethe subalgebras available in PDF, EPUB and Kindle. This book is based on the author's mini course delivered at Tokyo University of Marine Science and Technology in March 2019. The shuffle approach to Drinfeld-Jimbo quantum groups of finite type (embedding their "positive" subalgebras into q-deformed shuffle algebras) was first developed independently in the 1990s by J. Green, M. Rosso, and P. Schauenburg. Motivated by similar ideas, B. Feigin and A. Odesskii proposed a shuffle approach to elliptic quantum groups around the same time. The shuffle algebras in the present book can be viewed as trigonometric degenerations of the Feigin-Odesskii elliptic shuffle algebras. They provide combinatorial models for the "positive" subalgebras of quantum affine algebras in their loop realizations. These algebras appeared first in that context in the work of B. Enriquez. Over the last decade, the shuffle approach has been applied to various problems in combinatorics (combinatorics of Macdonald polynomials and Dyck paths, generalization to wreath Macdonald polynomials and operators), geometric representation theory (especially the study of quantum algebras' actions on the equivariant K-theories of various moduli spaces such as affine Laumon spaces, Nakajima quiver varieties, nested Hilbert schemes), and mathematical physics (the Bethe ansatz, quantum Q-systems, and quantized Coulomb branches of quiver gauge theories, to name just a few). While this area is still under active investigation, the present book focuses on quantum affine/toroidal algebras of type A and their shuffle realization, which have already illustrated a broad spectrum of techniques. The basic results and structures discussed in the book are of crucial importance for studying intrinsic properties of quantum affinized algebras and are instrumental to the aforementioned applications.
A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory
A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory write by Bangming Deng. This book was released on 2012-12-06. A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory available in PDF, EPUB and Kindle. The first book of its kind to present an algebraic approach to affine q-Schur algebras and affine quantum Schur-Weyl theory.
Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification
Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification write by Jacob Greenstein. This book was released on 2022-03-11. Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification available in PDF, EPUB and Kindle. 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.
Recent Developments in Quantum Affine Algebras and Related Topics
Recent Developments in Quantum Affine Algebras and Related Topics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recent Developments in Quantum Affine Algebras and Related Topics write by Naihuan Jing. This book was released on 1999. Recent Developments in Quantum Affine Algebras and Related Topics available in PDF, EPUB and Kindle. This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying "centre stage" in the theory of infinite dimensional Lie theory.
