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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 5 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1091737128

Digital Object Identifier
doi:10.1215/S0012-7094-01-10816-8

Mathematical Reviews number (MathSciNet)
MR1831824

Zentralblatt MATH identifier
1024.17008

Subjects
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

Citation

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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