Duke Mathematical Journal

Realization of level one representations of U q(g) at a root of unity

Vyjayanthi Chari and Naihuan Jing

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Using vertex operators, we construct explicitly Lusztig's ℤ[q,q−4]-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 character is given by the Weyl-Kac character formula.

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Duke Math. J., Volume 108, Number 1 (2001), 183-197.

First available in Project Euclid: 5 August 2004

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Zentralblatt MATH identifier

Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Secondary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras


Chari, Vyjayanthi; Jing, Naihuan. Realization of level one representations of $U\sb q(\hat{\mathfrak {g}})$ at a root of unity. Duke Math. J. 108 (2001), no. 1, 183--197. doi:10.1215/S0012-7094-01-10816-8. https://projecteuclid.org/euclid.dmj/1091737128

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