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We show that wonderful varieties are necessarily spherical (i.e., they are almost homogeneous under any Borel subgroup ofG).
      
We study certain naturally-defined analytic domains in the complexified groupHC which are invariant under left and right translation byH?.
      
As an example of how this can be used, we show that the ring of invariants (under the adjoint action of SL (3)) ofg copies ofM3 is C-M.
      
In this paper, we prove three types of rigidity results related to CAT(-1) spaces, namely the rigidity of the isometric actions on CAT(-1) spaces under the commensurability subgroups, the higher rank lattices and certain ergodic cocycles.
      
As an application, under the same assumption on the transitive group, we show that weakly symmetric spaces are precisely the homogeneous Riemannian manifolds with commutative algebra of invariant differential operators.
      
Here we provide certain conditions (more general than those in [Ka1]) which guarantee preservation of the topology under a modification.
      
We show that one can lift locally real analytic curves from the orbit space of a compact Lie group representation, and that one can lift smooth curves even globally, but under an assumption.
      
LetY be the space generated by the semi-invariants of under adjoint action.
      
Under the obvious restriction map, the space of biinvariants is proved isomorphic to the Weyl group invariants of the character group ring associated to the restricted roots.
      
Similar to Steinberg's connected and simply connected case [22] and under additional assumptions on the fundamental group of G, a global section to this quotient map exists.
      
A pattern for an element of a Weyl group is its image under a combinatorially defined map to a subgroup generated by reflections.
      
The complexity of a homogeneous space G/H under a reductive group G is by definition the codimension of general orbits in G/H of a Borel subgroup B\subseteq G.
      
The irreducibility of a subspace U ?= V under the κα implies that, for generic values of the parameter, the braid group Bg acts irreducibly on U.
      
We prove an effective commutativity criterion and classify Gelfand pairs under two mild technical constraints.
      
The new interpretation makes transparent for GLn (and conceivable for other classical groups) a certain invariance of Jantzen's sum formula under "Howe duality" in the sense of Adamovich and Rybnikov.
      
It is also shown that on the nilmanifold $\Gamma\backslash (H^3\times H^3)$ the balanced condition is not stable under small deformations.
      
We can prove these inequalities under weaker assumptions.
      
More precisely, we show that under some conditions on X, every such automorphism is of the form Φ = ?g, where ? is an algebraic action of a linear algebraic group G of dimension 1 on X, and where g belongs to G.
      
We also prove that under some minor assumptions the group of linear automorphisms preserving a given Legendrian subvariety preserves the contact structure of the ambient projective space.
      
This phenomena is related to the invariant cycles under the transformation We also give a characterization of all low-pass filters for MSF wavelets.
      
 

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