Realization of level one representations of U_q(\mathfrak g) at a root of unity

1999/09/21 by Vyjayanthi Chari, Naihuan Jing
Mathematics · #math.QA #math.RT #msc:17B

paper · pdf

published as Duke Math. J. 108 (2001), 183-197. · 13 pages

arxiv created 1999/09/21 · arxiv updated 2009/11/30

Abstract

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.

Related

• Level One Representations of Quantum Affine Algebras U_q(C⁽¹⁾_n)
• Level one representations of U_q(G₂⁽¹⁾)
• A construction of level 1 irreducible modules for U_q(sp₄) using level 2 intertwiners for U_q(sl₂)
• q-Vertex operators for quantum affine algebras
• The q-characters at roots of unity