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The method applies to the standard arithmetic subgroups ofSO(n,1) (a case which was proved previously by Millson [Mi]), to the nonarithmetic lattices inSO(n,1) constructed by Gromov and PiatetskiShapiro [GPS] and to groups generated by reflections.


We also show how to distinguish examples of open subsets with a good quotient coming from Mumford's theory and give examples of open subsets with nonquasiprojective quotients.


An algebraicGvarietyX is called "wonderful", if the following conditions are satisfied:X is (connected) smooth and complete;X containsr irreducible smoothGinvariant divisors having a non void transversal intersection;G has 2r orbits inX.


Lichtenstein in the caseu =(n, ?) or(n?), we prove that ?(q).ζ1/2 is non zero for all harmonic polynomialsq ∈S() \ {0}.


In [Ka1] its geometric counterpart was applied to construct contractible smooth affine varieties nonisomorphic to Euclidean spaces.


It is wellknown that the ring of invariants associated to a nonmodular representation of a finite group is CohenMacaulay and hence has depth equal to the dimension of the representation.


More generally, we prove that if Γ is an irreducible arithmetic noncocompact lattice in a higher rank group, then Γ containsf·g·p·d·f groups.


This construction is based on the notion of a certain duality between compact and noncompact homogeneous spaces.


Assuming that the surface contains two elliptic fibrations that are invariant by nonperiodic automorphisms, we give the classification of invariant probability measures.


Conjugacy classes of nonconnected semisimple algebraic groups


Consider a nonconnected algebraic group G = G ? Γ with semisimple identity component G and a subgroup of its diagram automorphisms Γ.


Invariant Theory for NonAssociative Real TwoDimensional Algebras and Its Applications


The set ${\mathcal A}$ of all nonassociative algebra structures on a fixed 2dimensional real vector space $A$ is naturally a ${\mbox{\rm GL}}(2,{\mbox{\bf R}})$module.


We show that the absolute invariants (i.e.,the ${\mbox{\rm GL}}(2, {\mbox{\bf R}})$invariants in the field of fractions of ${\mathcal P}$) distinguish the isomorphism classes of 2dimensional nonassociative real division algebras.


The main result of this paper is that there is a nonlinearizable real algebraic


We characterize, for finite measure spaces, those orthonormal bases with the following positivity property: if f is a nonnegative function, then the partial sums in the expansion of f are nonnegative.


This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the biorthogonal, i.e., nonunitary case.


In particular we give a nonprobabilistic proof of a Harnacktype principle, due to Ba?uelos et al.


Nondivergence form operators and variations on Yau's explosion criterion


Let ? denote the standard (i.e., LeviCivita) Laplacian for some noncompact, connected, complete, separable Riemannian manifild M.

