Quantized moduli spaces of the bundles on the elliptic curve and their applications

Details Quantized moduli spaces of the bundles on the elliptic curve and their applications Quantized moduli spaces of the bundles on the elliptic curve and their applications

1998-12-09

arxiv.org/abs/math/9812059v1

Mathematics

Quantum Algebra

21 pages, AMSTex

Scientific paper

We quantize the coordinate ring of the moduli space of B-bundles on the elliptic curve. Here B is a Borel subgroup of some semisimple Lie group. We construct some representations of these algebras and study intertwining operators for these representations. We apply our constructions to produce some objects: the elliptic Belavin R-matrix, the quantization of the algebra of functions on the Grassmannian, some generalized elliptic R-matrix. We consider also the affine case and write down the explicit formula for commuting elements.

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