Let $$ {\overline{\mathrm{X}}}_{\uplambda} be the closure of I-orbit in affine Grassmanian Gr a simple algebraic group G adjoint type, where I is Iwahori subgroup and λ coweight G. We find algorithm which describes set Ψ(λ) all I-orbits terms coweights. introduce R-operators (associated to positive roots) on lattice G, exactly describe relation I-orbits. These operators satisfy Braid relations ...

In this paper we study Zimmer's conjecture for $C^{1}$ actions of lattice subgroup a higher-rank simple Lie group with finite center on compact manifolds. We show that when the rank an uniform is larger than dimension manifold, then action factors through group. For lattices in ${\rm SL}(n, {{\mathbb {R}}})$ , dimensional bound sharp.

The author considers the problem of determining whether certain classes of lattice ordered groups (¿-groups) have the amalgamation property. It is shown that the classes of abelian totally ordered groups (ogroups) and abelian /-groups have the property, but that the class of ¿-groups does not. However, under certain cardinality restrictions one can find an ¿-group which is the "product" of /-gr...

We prove that every distributive algebraic lattice with at most א1 compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module. The א1 bound is optimal, as we find a distributive algebraic lattice D with א2 compact elements that is not isomorphic to the congruence lattice of any algebra with almost permutable congruences (hence n...

We use conference matrices to define an action of the complex numbers on the real Euclidean vector space R. In certain cases, the lattice D n becomes a module over a ring of quadratic integers. We can then obtain new unimodular lattices, essentially by multiplying the lattice D n by a non-principal ideal in this ring. We show that lattices constructed via quadratic residue codes, including the ...

We study the algebras of modular forms on type IV symmetric domains for simple lattices; that is, lattices which every Heegner divisor occurs as a Borcherds product. For lattice L signature (n,2) with 3≤n≤10, we prove graded algebra maximal reflection subgroup orthogonal group is freely generated. also show that, five exceptions, discriminant kernel

We consider Shimura varieties for orthogonal or spin groups acting on hermitian symmetric domains of type IV. give regular $p$ -adic integral models these over odd primes at which the level subgroup is connected stabilizer a vertex lattice in space. Our construction obtained by combining results Kisin and first author with an explicit presentation resolution corresponding local model.

A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion...

We study a three dimensional Z(3)-symmetric effective theory of high temperature QCD. The exact lattice-continuum relations, needed in order to perform lattice simulations with physical parameters, are computed to order O(a 0) in lattice perturbation theory. Lattice simulations are performed to determine the phase structure of a subset of the parameter space. Z(3)-symmetric effective theory of ...

B (∗) s ) are well known experimentally, and thus provide a testing ground for the lattice method. In particular, they can be used to examine the convergence properties of the heavy quark expansion in nonrelativistic QCD (NRQCD),[1] which is the most economical lattice action available for heavy quark physics.[2] The spectrum of P-wave heavy-light mesons is not yet understood, experimentally no...