Finite-dimensional representations of quantum affine algebras at roots of unity

Jonathan Beck, Victor G. Kac

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


We describe explicitly the canonical map χ : Spec Uε(g̃) → Spec Zε, where Uε(g̃) is a quantum loop algebra at an odd root of unity ε. Here Zε is the center of Uε(g̃) and Spec R stands for the set of all finite- dimensional irreducible representations of an algebra R. We show that Spec Zε is a Poisson proalgebraic group which is essentially the group of points of G over the regular adeles concentrated at 0 and ∞. Our main result is that the image under χ of Spec Uε(g̃) is the subgroup of principal adeles.

Original languageEnglish
Pages (from-to)391-423
Number of pages33
JournalJournal of the American Mathematical Society
Issue number2
StatePublished - Apr 1996
Externally publishedYes


Dive into the research topics of 'Finite-dimensional representations of quantum affine algebras at roots of unity'. Together they form a unique fingerprint.

Cite this