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In our paper [KR] we began a systematic study of representations of the universal central extension[InlineEquation not available: see fulltext.] of the Lie algebra of differential operators on the circle.
      
This study was continued in the paper [FKRW] in the framework of vertex algebra theory.
      
In the present paper we study the remaing nontrivial case, that of a negative central charge-N.
      
We study reductive group actions on complex affine quadrics.
      
We study certain naturally-defined analytic domains in the complexified groupHC which are invariant under left and right translation byH?.
      
We study the multiplicative structure of rings of coinvariants for finite groups.
      
This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry.
      
We study Edidin and Graham's equivariant Chow groups in the case of torus actions.
      
We study the tensor category of tilting modules over a quantum groupUq with divided powers.
      
The main idea for our approach relies on a study of the boundary theory we established for the general CAT(-1) spaces.
      
The aim of the paper is the study of the orbits of the action of PGL4 on the space ?3 of the cubic surfaces of ?3, i.e., the classification of cubic surfaces up to projective motions.
      
We study discrete (Kleinian) subgroups of the isometry group Iso+H4 of the real hyperbolic space of dimension 4.
      
We study the modificationA→A' of an affine domainA which produces another affine domainA'=A[I/f] whereI is a nontrivial ideal ofA andf is a nonzero element ofI.
      
We also study the structure of the exceptional?-graded transitive Lie superalgebras and give their geometric realization.
      
We study Cartier divisors on normal varieties with the action of a reductive groupG.
      
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 aG-variety.
      
We study their general properties and apply these results to Schubert varieties.
      
We introduce and study the notion of essential dimension for linear algebraic groups defined over an algebraically closed fields of characteristic zero.
      
In the course of the proof we show that one can reduce the study of generating semi-invariants to the case when the quiver has no oriented paths of length greater than one.
      
We study the Filiform Lie Groups admitting a left invariant affine structure.
      
 

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