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- W2138049488 abstract "We prove the Macdonald conjecture of Hanlon and Feigin for reductive groups G. In a geometric reformulation, we show that the Dolbeault cohomology Hq(X;Op) of the loop Grassmannian X is freely generated by de Rham's forms on the disk coupled to the indecomposables of H·(BG). Equating the two Euler characteristics gives an identity, independently known to Macdonald [M], which generalises Ramanujan's 1?1 sum. For simply laced root systems at level 1, we also find a strong form of Bailey's 4?4 sum. Failure of Hodge decomposition implies the singularity of X, and of the algebraic loop groups. Some of our results were announced in [T2]." @default.
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- W2138049488 date "2008-07-01" @default.
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- W2138049488 title "The strong Macdonald conjecture and Hodge theory on the loop Grassmannian" @default.
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- W2138049488 doi "https://doi.org/10.4007/annals.2008.168.175" @default.
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