Shuffle Approach Towards Quantum Affine and Toroidal Algebras
Shuffle Approach Towards Quantum Affine and Toroidal Algebras
English | 2023 | ISBN: 9819931495 | 130 Pages | PDF EPUB (True) | 16 MB
English | 2023 | ISBN: 9819931495 | 130 Pages | PDF EPUB (True) | 16 MB
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.