dorsal/arxiv
View SchemaQuantum Affine Algebras at Roots of Unity
| Authors | Vyjayanthi Chari, Andrew Pressley |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9609031 |
| URL | https://arxiv.org/abs/q-alg/9609031 |
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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"abstract": "We study the restricted form of the qaunatized enveloping algebra of an\nuntwisted affine Lie algebra and prove a triangular decomposition for it. In\nproving the decomposition we prove several new identities in the quantized\nalgebra, one of these show a connection between the quantized algebra and Young\ndiagrams. These identities are all invisible in the non-quantum case of the\nproblem which was considered by Garland in 1978. We then study the\nfinite-dimensional irreducible representations and prove a factorization\ntheorem for such representations.",
"arxiv_id": "q-alg/9609031",
"authors": [
"Vyjayanthi Chari",
"Andrew Pressley"
],
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"q-alg",
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"title": "Quantum Affine Algebras at Roots of Unity",
"url": "https://arxiv.org/abs/q-alg/9609031"
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