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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On representations of affine Kac-Moody
groups and related loop groups


Author: Yu Chen
Journal: Trans. Amer. Math. Soc. 348 (1996), 3733-3743
MSC (1991): Primary 17B67, 20C15, 22E70
MathSciNet review: 1361638
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Abstract: We demonstrate a one to one correspondence between the irreducible projective representations of an affine Kac-Moody group and those of the related loop group, which leads to the results that every non-trivial representation of an affine Kac-Moody group must have its degree greater than or equal to the rank of the group and that the equivalence appears if and only if the group is of type $A_{n}^{(1)}$ for some $n\ge 1$. Moreover the characteristics of the base fields for the non-trivial representations are found being always zero.


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Additional Information

Yu Chen
Affiliation: Dipartimento di Matematica, Università di Torino, Via C. Alberto 10, 10123 Torino, Italy
Email: yuchen@dm.unito.it

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01677-7
PII: S 0002-9947(96)01677-7
Keywords: Kac-Moody group, loop group, Chevalley-Demazure group scheme, minimal representation
Received by editor(s): August 4, 1995
Additional Notes: Research supported in part by the Italian M.U.R.S.T. and C.N.R.-G.N.S.A.G.A
Dedicated: Dedicated to Professor G. Zacher on the occasion of his seventieth birthday
Article copyright: © Copyright 1996 American Mathematical Society