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Cyclic homology and the Macdonald conjectures

Hanlon, Phil

Hanlon, Phil

1986-02

Citation:Hanlon, Phil; (1986). "Cyclic homology and the Macdonald conjectures." Inventiones Mathematicae 86(1): 131-159. <http://hdl.handle.net/2027.42/46617>

Abstract: Let A+(k) denote the ring ℂ[ t ]/ t k+1 and let G be a reductive complex Lie algebra with exponents m 1 , ..., m n . This paper concerns the Lie algebra cohomology of G ⊗ A + ( k ) considered as a bigraded algebra (here one of the gradings is homological degree and the other, which we call weight , is inherited from the obvious grading of G ⊗ A + ( k )). We conjecture that this Lie algebra cohomology is an exterior algebra with k +1 generators of homological degree 2 m s +1 for s =1,2, ..., n . Of these k +1 generators of degree 2 m s +1, one has weight 0 and the others have weights ( k +1) m s +t for t =1,2, ..., k .