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

Abstract

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.