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In this paper we provide, under some mild explicit assumptions, a geometricdescription of the category of representations of the centralizer of a regularunipotent element in a reductive algebraic group in terms of perverse sheaveson the Langlands dual affine flag variety. This equivalence is suggested andmotivated by the "geometric Langlands" philosophy.

Modular affine Hecke category and regular unipotent centralizer, I