The big projective module as a nearby cycles sheaf

Justin Campbell ^[1]
1. [1] Cambridge, MA
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 1, 2017, págs. 721-726
Idioma: inglés
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Resumen
- We give a new geometric construction of the big projective module in the principal block of the BGG category O, or rather the corresponding D-module on the flag variety. Namely, given a one-parameter family of nondegenerate additive characters of the unipotent radical of a Borel subgroup which degenerate to the trivial character, there is a corresponding one-parameter family of Whittaker sheaves. We show that the unipotent nearby cycles functor applied to this family yields the big projective D-module.