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Shuffle Approach Towards Quantum Affine and Toroidal Algebras by Alexander Tsymbaliuk is a nonfiction available to read on EtoBox.

What is Shuffle Approach Towards Quantum Affine and Toroidal Algebras about?

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, Nak

Who reads Shuffle Approach Towards Quantum Affine and Toroidal Algebras?

Author

Alexander Tsymbaliuk

Publisher

Springer Nature Singapore Pte Ltd Fka Springer Science + Business Media Singapore Pte Ltd

Published

2023

Language

EN

ISBN

9789819931491

Category

nonfiction

Subjects

Mathematics, Science, Physics