Realization of level one representations of $U_q(\hat{\mathfrak g})$ at a root of unity

Details Realization of level one representations of $U_q(\hat{\mathfrak g})$ at a root of unity Realization of level one representations of $U_q(\hat{\mathfrak g})$ at a root of unity

1999-09-21

arxiv.org/abs/math/9909118v1

Duke Math. J. 108 (2001), 183-197.

Mathematics

Quantum Algebra

13 pages

Scientific paper

Using vertex operators, we construct explicitly Lusztig's $\mathbb Z[q, q^{-1}]$-lattice for the level one irreducible representations of quantum affine algebras of ADE type. We then realize the level one irreducible modules at roots of unity and show that the q-dimension is still given by the Weyl-Kac character formula. As a consequence we also answer the corresponding question of realizing the affine Kac-Moody Lie algebras of simply laced type at level one in finite characteristic.

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