Finite dimensional representations of quantum affine algebras

Mar 29, 1994
17 pages
Published in:
  • J.Phys.A 28 (1995) 1915-1928
e-Print:
Report number:
  • UQMATH-94-01

Citations per year

19931995199719991999130
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 q=1q=1 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 q=1q = 1. 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.