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This underlying group H1(X, T \bar{X}) can be described as a generalized Prym variety, whose connected component is either an abelian variety or a degenerate abelian variety.
      
The F-valued points of the algebra ofstrongly regular functions of a Kac-Moody group
      
Let G be a simply connected semisimple complex Lie group and fix a maximal
      
From Lie algebras of vector fields to algebraic group actions
      
The action of an affine algebraic group G on an algebraic variety V can be
      
Let H be a semisimple algebraic group and let X be a smooth projective curve
      
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.
      
As a consequence, there is either a unique set, or an (almost) unique two-parameter set of Weyl group invariant quantum zonal spherical functions associated to an irreducible symmetric pair.
      
We study tensor products Vλ ? Vμ of irreducible representations of a connected, simply-connected, complex reductive group G.
      
Consider a non-connected algebraic group G = G ? Γ with semisimple identity component G and a subgroup of its diagram automorphisms Γ.
      
Let T be a τ -stable maximal torus of G and its Weyl group W.
      
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.
      
This map corresponds geometrically to restriction to the fixed point set of an action of a one-dimensional torus on the flag variety of a semisimple group G.
      
Ergodicity of mapping class group actions on representation varieties, II.
      
The mapping class group of a compact oriented surface of genus greater than
      
Our basic tool is the representation theory of the Burkhardt group G = G25 920, which acts on our varieties.
      
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.
      
Let g be a complex, simple Lie algebra with Cartan subalgebra h and Weyl group W.
      
The corresponding monodromyre presentation of the braid group Bg of type g is a deformation of the action of (afinite extension of) W on V.
      
 

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