ar X iv : q - a lg / 9 70 70 31 v 1 2 4 Ju l 1 99 7 DOUBLE QUANTIZATION ON THE COADJOINT REPRESENTATION OF

ar X iv : q - a lg / 9 70 70 31 v 2 1 2 O ct 1 99 7 DOUBLE QUANTIZATION ON THE COADJOINT REPRESENTATION OF SL

For g = sl(n) we construct a two parametric U h (g)-invariant family of algebras, (Sg) t,h , which defines a quantization of the function algebra Sg on the coadjoint representation and in the parameter t gives a quantization of the Lie bracket. The family induces a two parametric deformation of the function algebra of any maximal orbit which is a quantization of the Kirillov-Kostant-Souriau bra...

ar X iv : q - a lg / 9 60 70 28 v 1 2 7 Ju l 1 99 6 Examples of Categorification

ar X iv : m at h - ph / 9 80 70 27 v 1 2 4 Ju l 1 99 8 Strict quantization of coadjoint orbits

A strict quantization of a compact symplectic manifold S on a subset I ⊆ R, containing 0 as an accumulation point, is defined as a continuous field of C *-algebras {A } ∈I , with A0 = C0(S), and a set of continuous cross-sections {Q(f)} f ∈C ∞ (S) for which Q0(f) = f. Here Q (f *) = Q (f) * for all ∈ I, whereas for → 0 one requires that i[Q (f), Q (g)]/ → Q ({f, g}) in norm. We discuss general ...

ar X iv : a lg - g eo m / 9 70 70 16 v 1 2 5 Ju l 1 99 7 RATIONAL CURVES ON QUASI - PROJECTIVE SURFACES

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ar X iv : q - a lg / 9 70 90 01 v 1 1 S ep 1 99 7 Bilinear identity for q - hypergeometric integrals