We consider the problem of finding Clifford-Klein forms in a class of homogeneous spaces determined by inclusions of real Lie algebras of a special type which we call strongly regular. This class of inclusions is described in terms of their Satake diagrams. For example, the complexifications of such inclusions contain the class of subalgebras generated by automorphisms of finite order. We show ...

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...

We classify the irreducible, admissible, smooth, genuine mod p representations of the metaplectic double cover of SL2(F ), where F is a p-adic field and p 6= 2. We show, using a generalized Satake transform, that each such representation is isomorphic to a certain explicit quotient of a compact induction from a maximal compact subgroup by an action of a spherical Hecke operator, and we define a...

Let G denote a connected reductive group over a nonarchimedean local field F . Let K denote a special maximal parahoric subgroup of G(F ). We establish a Satake isomorphism for the Hecke algebra HK of K-bi-invariant compactly supported functions on G(F ). The key ingredient is a Cartan decomposition describing the double coset space K\G(F )/K. We also describe how our results relate to the trea...

For a simply-connected simple algebraic group G over C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of G, generalizing a well-known fact about GLn. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number ...

Using the Kuga-Satake correspondence we provide an effective algorithm for the computation of the Picard and Brauer groups of K3 surfaces of degree 2 over number fields.

The critical phylogenetic position of ascidians suggests that evolutionary origins of neuropeptides and hormones of vertebrates are highly likely to be conserved in ascidians, and the cosmopolitan species, Ciona intestinalis, is expected to be an excellent deuterostome invertebrate model for studies on neuropeptides and hormones of vertebrates. Nevertheless, molecular and functional characteriz...