Unitary representations and modular actions.

Kechris, A.S.

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In this paper we calculate the 2-modular character table of the twisted Chevalley group 2D4(2) using computer techniques available in an algebra package called Meat-Axe. This package is now available in Mu'tah University as well as other universities such as Birmingham University in the UK and Aachen University in Germany. The determination of this character table will be a contribution to modular calculations of various simple groups.

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Let E₀ be the Vitali equivalence relation and E₃ the product of countably many copies of E₀. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel equivalence relation E that is (Borel) reducible to E₃, either E is reducible to E₀ or else E₃ is reducible to E. Second, if E is a Borel equivalence relation induced by a Borel action of a closed subgroup of the infinite symmetric group that admits an invariant metric, then either E is reducible...