Let T_n be the maximal torus of diagonal matrices in GL_n, t_n be the Lie algebra of T_n and let N_n=N_{GL_n}(T_n) be the normalizer of T_n in GL_n. Consider then the quotient stacks [t_n/N_n] and [gl_n/GL_n] for the conjugation actions. In this paper we construct an equivalence I:D_c^b([t_n/N_n]) --> D_c^b([gl_n/GL_n]) between the bounded derived categories of constructible l-adic sheaves.
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