Geometrizing the Minimal Representations of Even Orthogonal Groups
نویسندگان
چکیده
Let X be a smooth projective curve. Write BunSO2n for the moduli stack of SO2n-torsors on X. We give a geometric interpretation of the automorphic function f on BunSO2n corresponding to the minimal representation. Namely, we construct a perverse sheaf KH on BunSO2n such that f should be equal to the trace of the Frobenius of KH plus some constant function. The construction is based on some explicit geometric formulas for the Fourier coefficients of f on one hand, and on the geometric theta-lifting on the other hand. Our construction makes sense for more general simple algebraic groups, we formulate the corresponding conjectures. They could provide a geometric interpretation of some unipotent automorphic representations in the framework of the geometric Langlands program.
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