Euler characteristics of the generalized Kloosterman sheaves for symplectic and orthogonal groups
Abstract
We study the monodromy of certain -adic local systems attached to the generalized Kloosterman sheaves constructed by Yun and calculate their Euler characteristics under standard representations in the cases of symplectic and split/quasi-split orthogonal groups. This provides evidence for the conjectural description of their Swan conductors at ∞ which is predicted by Reeder-Yu on the Langlands parameters attached to the epipelagic representations.
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