give 
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.


In particular, we give a detailed description of these sets in terms of crosssections inside maximal Rtori ofH.


We develop methods that give rise to natural monomial bases for such rings over their ground fields and explicitly determine precisely which monomials are zero in the ring of coinvariants.


We give explicit systems of generators of the algebras of invariant polynomials in arbitrary many vector variables for the classical reflection groups (including the dihedral groups).


We also compute the Euler characteristic of the space of partial flags containingnt and give a connection with hyperplane arrangements.


We give a characterization of those elements ofW whose reduced expressions avoid substrings of the formsts wheres andt are noncommuting generators.


We give as an application a family of singular Schubert varieties.


We give complete proofs of the Ktheoretic construction of the quantized enveloping algebra of affine gl(n) sketched in [GV].


We then give a combinatorial classification of reductive monoids by means of the theory of spherical varieties.


We also study the structure of the exceptional?graded transitive Lie superalgebras and give their geometric realization.


We give criteria for a divisor to be Cartier, globally generated and ample, and apply them to a study of the local structure and the intersection theory of aGvariety.


In this paper we give a full set of simple moves and relations which turnM(Σ) into a connected and simplyconnected 2complex.


In the last section we give an exposition of results, communicated to us by J.P.


Indeed, we will give a full classification of the manifoldsN(g, V) which are commutative spaces, using a characterization in terms of multiplicityfree actions.


Moreover, we give a uniform description of the algebras of semiinvariants of Euclidean quivers.


Fork=1, we give explicit formulas for the characters.


We give the classification of all finite dimensional LeviTanaka algebras of CR codimension two and construct the corresponding standard homogeneous CR manifolds.


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


We also describe the closure of orbits and then give applications to the repartition of rational points on K3 surfaces.


In this paper we give a characterization of symmetric Siegel domains in terms of a certain norm equality which involves a Cayley transform.

