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We define a map from an affine Weyl group to the set of conjugacy classes of an ordinary Weyl group.
      
We show that they are induced by automorphisms ofG and that a surjective holomorphic self-map can be nonbijective only in the directions of the nilradical ofG.
      
We modify the Hochschild φ-map to construct central extensions of a restricted Lie algebra.
      
Iff1,f2 generate this ring, the quotient map of φ is the mapF:?3→?2,x?(f1(x), f2(x)).
      
An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient
      
We then show that there is a unique order-reversing duality map No,c → LNo,c that has certain properties analogous to those of the original Lusztig-Spaltenstein duality map.
      
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.
      
Furthermore, exploiting the Jordan decomposition, the reduced fibres of this quotient map are naturally associated bundles over semisimple G-orbits.
      
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.
      
It is known [7] that dualizing a form of the Poisson summation formula yields a pair of linear transformations which map a function ? of one variable into a function and its cosine transform in a generalized sense.
      
A wandering set for a map ? is a set containing precisely one element from each orbit of ?.
      
In signal processing, communications, and other branches of information technologies, it is often desirable to map the higher-dimensional signals on Sn.
      
In this paper, the topological pressure is preserved under some semi-conjugates, and a formula of computing topological pressure by use of periodic points for positively expansive continuous map with specification is given.
      
In this paper, we will discuss the construction problems about the invariant sets and invariant measures of continuous maps which map complexes into themselves, using simplicial approximation and Markov chains.
      
We also construct an invariant set that is the chain-recurrent set of the map by means of a non-negative matrix which only depends on the map.
      
autgH/*)) is investigated by using bundle map theory and transformation group theory.
      
A Halin map is a kind of planar maps oriented by a tree.
      
Sinai-bowen-ruelle measure and the structure of strange attractors in the Lauwerier map
      
 

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