Shuffle Approach Towards Quantum Affine and Toroidal Algebras

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.