Finite dimensional representations of quantum affine algebras
Mar 29, 199417 pages
Published in:
- J.Phys.A 28 (1995) 1915-1928
e-Print:
- hep-th/9403162 [hep-th]
Report number:
- UQMATH-94-01
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Abstract:
We give a general construction for finite dimensional representations of U_q(\hat{\G}) where \hat{\G} is a non-twisted affine Kac-Moody algebra with no derivation and zero central charge. At this is trivial because U(\hat{\G})=U({\G})\otimes \C(x,x~{-1}) with \G a finite dimensional Lie algebra. But this fact no longer holds after quantum deformation. In most cases it is necessary to take the direct sum of several irreducible U_q({\G})-modules to form an irreducible U_q(\hat{\G})-module which becomes reducible at . We illustrate our technique by working out explicit examples for \hat{\G}=\hat{C}_2 and \hat{\G}=\hat{G}_2. These finite dimensional modules determine the multiplet structure of solitons in affine Toda theory.References(15)
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