Let G be finite group and K a number field or a p-adic field with ring of integers O K . In the first part of the manuscript we present an algorithm that computes the relative algebraicas an abstract abelian group. We also give algorithms to solve the discrete logarithm problems in, K) and in the locally free class group cl(O K [G]). All algorithms have been implemented in Magma for the case K = Q.In the second part of the manuscript we prove formulae for the torsion subgroup of K 0 (Z[G], Q) for large classes of dihedral and quaternion groups.

Abstract. The Verlinde formula is computed for each of the simply-connected classical Lie groups, and it is shown that the resulting formula obeys certain reciprocity laws with respect to the exchange of the rank and the level. Some corresponding dualities between spaces of sections of theta line bundles over moduli spaces of G-bundles on curves are conjectured but not proved.

No abstract

Some empirical results on the cubic algebra 2a { = Σ [#/, [#/> ^]] are j presented. The algebra is satisfied at the residue of any pole in a solution to Nahm's non-self-dual equations.

No abstract