Quantum affine algebras at roots of unity
Authors:
Vyjayanthi Chari and Andrew Pressley
Journal:
Represent. Theory 1 (1997), 280328
MSC (1991):
Primary 17B67
Published electronically:
August 14, 1997
MathSciNet review:
1463925
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Abstract: Let be the quantized universal enveloping algebra of the affine Lie algebra associated to a finitedimensional complex simple Lie algebra , and let be the subalgebra of generated by the divided powers of the Chevalley generators. Let be the Hopf algebra obtained from by specialising to a nonzero complex number of odd order. We classify the finitedimensional irreducible representations of in terms of highest weights. We also give a ``factorisation'' theorem for such representations: namely, any finitedimensional irreducible representation of is isomorphic to a tensor product of two representations, one factor being the pullback of a representation of by Lusztig's Frobenius homomorphism , the other factor being an irreducible representation of the Frobenius kernel. Finally, we give a concrete construction of all of the finitedimensional irreducible representations of . The proofs make use of several interesting new identities in .
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Additional Information
Vyjayanthi Chari
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521
Email:
chari@math.ucr.edu
Andrew Pressley
Affiliation:
Department of Mathematics, King’s College, Strand, London WC2R 2LS, UK
Email:
anp@mth.kcl.ac.uk
DOI:
http://dx.doi.org/10.1090/S1088416597000307
PII:
S 10884165(97)000307
Received by editor(s):
April 30, 1997
Published electronically:
August 14, 1997
Additional Notes:
The first author was partially supported by NATO and EPSRC (GR/K65812)
The second author was partially supported by NATO and EPSRC (GR/L26216)
Article copyright:
© Copyright 1997
American Mathematical Society
