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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 non-arithmetic lattices inSO(n,1) constructed by Gromov and Piatetski-Shapiro [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 non-quasi-projective quotients.
      
An algebraicG-varietyX is called "wonderful", if the following conditions are satisfied:X is (connected) smooth and complete;X containsr irreducible smoothG-invariant 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 non-isomorphic to Euclidean spaces.
      
It is well-known that the ring of invariants associated to a non-modular representation of a finite group is Cohen-Macaulay and hence has depth equal to the dimension of the representation.
      
More generally, we prove that if Γ is an irreducible arithmetic non-cocompact 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 non-compact homogeneous spaces.
      
Assuming that the surface contains two elliptic fibrations that are invariant by non-periodic automorphisms, we give the classification of invariant probability measures.
      
Conjugacy classes of non-connected semisimple algebraic groups
      
Consider a non-connected algebraic group G = G ? Γ with semisimple identity component G and a subgroup of its diagram automorphisms Γ.
      
Invariant Theory for Non-Associative Real Two-Dimensional Algebras and Its Applications
      
The set ${\mathcal A}$ of all non-associative algebra structures on a fixed 2-dimensional 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 2-dimensional non-associative real division algebras.
      
The main result of this paper is that there is a non-linearizable real algebraic
      
We characterize, for finite measure spaces, those orthonormal bases with the following positivity property: if f is a non-negative function, then the partial sums in the expansion of f are non-negative.
      
This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the biorthogonal, i.e., non-unitary case.
      
In particular we give a non-probabilistic proof of a Harnack-type principle, due to Ba?uelos et al.
      
Non-divergence form operators and variations on Yau's explosion criterion
      
Let ? denote the standard (i.e., Levi-Civita) Laplacian for some non-compact, connected, complete, separable Riemannian manifild M.
      
 

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