A. Satake: <I>Die Offenbarung des Johannes I-III</I>

I Iiii a Reconceptualization of Anxiety

A generalization of the Kuga-Satake construction

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...

On the Satake Isomorphism

In this paper, we present an expository treatment of the Satake transform. This gives an isomorphism between the spherical Hecke algebra of a split reductive group G over a local field and the representation ring of the dual group Ĝ. If one wants to use the Satake isomorphism to convert information on eigenvalues for the Hecke algebra to local L-functions, it has to be made quite explicit. This...

Johannes Holtfreter

Twisted Geometric Satake Equivalence

Let k be an algebraically closed field and O = k[[t]] ⊂ F = k((t)). For an almost simple algebraic group G we classify central extensions 1 → Gm → E → G(F) → 1, any such extension splits canonically over G(O). Fix a positive integer N and a primitive character ζ : μN (k) → Q ∗ l (under some assumption on the characteristic of k). Consider the category of G(O)biinvariant perverse sheaves on E wi...