Quantum Affine Algebras at Roots of Unity

Vyjayanthi Chari; Andrew Pressley

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Quantum Affine Algebras at Roots of Unity

Vyjayanthi Chari·Andrew Pressley

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Abstract

We study the restricted form of the qaunatized enveloping algebra of an untwisted affine Lie algebra and prove a triangular decomposition for it. In proving the decomposition we prove several new identities in the quantized algebra, one of these show a connection between the quantized algebra and Young diagrams. These identities are all invisible in the non-quantum case of the problem which was considered by Garland in 1978. We then study the finite-dimensional irreducible representations and prove a factorization theorem for such representations.

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BibTeX RIS

Vyjayanthi Chari, Andrew Pressley. 1997-04-22. Quantum Affine Algebras at Roots of Unity. https://arxiv.org/abs/q-alg/9609031

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