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Simple finite dimensional Kantor triple systems are classified in terms of Satake diagrams. We prove that every simple linearly compact Kantor triple system is finite dimensional and provide an explicit presentation of all the classical and exceptional systems.

We give a generalization to higher genera of the famous formula 12 λ = δ for genus 1. We also compute the classes of certain strata in the Satake compactification as elements of the push down of the tautological ring.

We construct a normal projective rigid analytic compactification of an arbitrary Drinfeld modular variety whose boundary is stratified by varieties smaller dimensions. This generalizes work Kapranov. Using algebraic that Pink and Schieder's, we show the naturally isomorphic to analytification Pink's compactification. interpret forms as global sections natural ample invertible sheaves on deduce ...

Theorem 1. The convolution ∗ admits a commutativity constraint making Sph into a rigid tensor category. There exists a faithful, exact tensor “fiber” functor Sat : Sph → Vect inducing an equivalence (modulo a sign in the commutativity constraint) of Sph with Rep(G) as tensor categories, where G is the Langlands dual group of the reductive group G, whose weights are the coweights of G and vice v...

The Kuga-Satake construction [3] associates to a polarized Hodge structure H of weight 2 with h2,0 = 1 an abelian variety A which satisfies the property that H is a sub-Hodge structure of Hom (H1(A),H1(A)). The construction is very tricky and intriguing geometrically: one first associates to the lattice (H,<,>) its Clifford algebra C(H), which is again a lattice. Then one constructs a complex s...

The geometric Satake correspondence can be regarded as a construction of rational representations complex connected reductive group $G$. In their study this correspondence, Mirković and Vilonen introduced algebraic cycles that provide linear basis in each irreducible representation. Generalizing construction, Goncharov Shen define tensor product representations. We investigate these bases show ...