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

Let b be the Borelsubalgebra ofsom e Kac-M oody algebra g and B the corresponding group. (If b is in nite-dim ensional, then B is a projective lim it of nite-dim ensionalgroups). LetM (E;b)be the m odulispace ofB -bundleson the elliptic curve E. There is the naturalm ap B ! H ,where H is a Cartan subgroup,so each B -bundle de nesan H -bundle.Note,thateach H -bundle on E has the characteristic class which lies in H (E;L) = L,where L is the rootlattice of Kac-M oody algebra g. Foreach n 2 L we denote by M n(E;b)the corresponding connected com ponentofM (E;b). In [3]wede netheHam iltonian structureon them anifold M (E;b)and quantize