A reductive Q-simple algebraic group G is of hermitian type, if the symmetric space D defined by G(R) is a hermitian symmetric space. A discrete subgroup Γ ⊂ G(Q) is arithmetic, if for some faithful rational representation ρ : G −→ GL(V ), and for some lattice VZ ⊂ VQ, Γ is commensurable with ρ−1(GL(VZ)). A non-compact hermitian symmetric space is holomorphically equivalent to a bounded symmetr...

We construct various modular compactifications of the space elliptic K3 surfaces using tools from minimal model program, and explicitly describe parametrized by their boundaries. The coarse spaces our constructed admit morphisms to Satake-Baily-Borel compactification. Finally, we show that one is smooth with GIT quotient pairs Weierstrass a chosen fiber.

Abstract We apply Treumann’s “Smith theory for sheaves” in the context of Iwahori–Whittaker model Satake category. deduce two results representation reductive algebraic groups over fields positive characteristic: (a) a geometric proof linkage principle; (b) character formula tilting modules terms $\ell $ ℓ -c...

M. Gounelle, T. Mikouchi, K. Ohsumi, M. K. Weisberg, L. Le, W. Satake & T. Kurihara, ARES, NASA Johnson Space Center, Houston, TX 77058, USA ([email protected]); Muséum National d’Histoire Naturelle, 57, rue Cuvier, 75005, Paris, France; University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; Kingsborough Community College, Brooklyn, NY 11235, USA; Department of Earth and Planet...

The modular variety of non singular and complete hyperelliptic curves with level-two structure of genus 3 is a 5-dimensional quasi projective variety which admits several standard compactifications. The first one comes from the period map, which realizes this variety as a sub-variety of the Siegel modular variety of level two and genus three H3/Γ3[2]. We denote the hyperelliptic locus by I3[2] ...

We extend the noncommutative geometry model of the fractional quantum Hall effect, previously developed by Mathai and the first author, to orbifold symmetric products. It retains the same properties of quantization of the Hall conductance at integer multiples of the fractional Satake orbifold Euler characteristics. We show that it also allows for interesting composite fermions and anyon represe...