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characteristic    
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  characteristic
We use the theory of tilting modules for algebraic groups to propose a characteristic free approach to "Howe duality" in the exterior algebra.
      
Euler characteristic of certain affine flag varieties
      
The purpose of this note is to prove, as Lusztig stated, that the Euler characteristic of the variety of Iwahori subalgebras containing a certain nil-elliptic elementnt istcl wherel is the rank of the associated finite type Lie algebra.
      
For the case of positive characteristic we use the classification of finite irreducible groups generated by pseudoreflections due to Kantor, Wagner, Zalesski? and Sere?kin.
      
We also compute the Euler characteristic of the space of partial flags containingnt and give a connection with hyperplane arrangements.
      
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