Finite-dimensional representations of
quantum affine algebras at roots of unity
Authors:
Jonathan Beck and Victor G. Kac
Journal:
J. Amer. Math. Soc. 9 (1996), 391-423
MSC (1991):
Primary 17B37, 81R50
DOI:
https://doi.org/10.1090/S0894-0347-96-00183-X
MathSciNet review:
1317228
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We describe explicitly the canonical map Spec
Spec
, where
is a quantum loop algebra at an odd root of unity
. Here
is the center of
and Spec
stands for the set of all finite--dimensional irreducible representations of an algebra
. We show that Spec
is a Poisson proalgebraic group which is essentially the group of points of
over the regular adeles concentrated at and
. Our main result is that the image under
of Spec
is the subgroup of principal adeles.
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Additional Information
Jonathan Beck
Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email:
beck@math.harvard.edu
Victor G. Kac
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email:
kac@math.mit.edu
DOI:
https://doi.org/10.1090/S0894-0347-96-00183-X
Received by editor(s):
October 28, 1994
Received by editor(s) in revised form:
November 9, 1994
Additional Notes:
The first author was supported by an NSF Postdoctoral Fellowship.
The second author was supported in part by NSF grant DMS–9103792.
Article copyright:
© Copyright 1996
American Mathematical Society