Resumen de Epipelagic representations and rigid local systems

Zhiwei Yun

• We construct automorphic representations for quasi-split groups G over the function field F=k(t)F=k(t) one of whose local components is an epipelagic representation in the sense of Reeder and Yu. We also construct the attached Galois representations under the Langlands correspondence. These Galois representations give new classes of conjecturally rigid, wildly ramified LGLG -local systems over P1−{0,∞}P1−{0,∞} that generalize the Kloosterman sheaves constructed earlier by Heinloth, Ngô and the author. We study the monodromy of these local systems and compute all examples when G is a classical group.