Analysis determines Hecke algebra spectrum for the unramified Eisenstein series in global fields, suggesting implications for derived quotient stack theories.
For a split reductive group L G { }L G over a global field, we determine the spectrum of the spherical Hecke algebra coming from the unramified Eisenstein series for the minimal parabolic L B { }L B . This is done using a certain decomposition of the Springer stack T ∗ ( B ∖ G / B ) T^*(B G/B) for the Langlands dual group G G in the additive cobordism group of cohomologically proper derived quotient stacks.
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Kazhdan et al. (2025) studied this question.
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