New nonabelian shift operators and wall-crossing identities show that the quantized Coulomb branch of pure GL_n gauge theory is a quotient of the shifted Yangian Y_{-nα}(sl2), with vertex functions as Hecke eigenfunctions.
On the unramified Eisenstein spectrum
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abstract
For a split reductive group ${}^L G$ over a global field, we determine the spectrum of the spherical Hecke algebra coming from the unramified Eisenstein series for the minimal parabolic ${}^L B$. This is done using a certain decomposition of the Springer stack $T^*(B \backslash G/ B)$ for the Langlands dual group in the additive group of cobordisms of cohomologically proper derived quotient stacks.
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Nonabelian shift operators and shifted Yangians
New nonabelian shift operators and wall-crossing identities show that the quantized Coulomb branch of pure GL_n gauge theory is a quotient of the shifted Yangian Y_{-nα}(sl2), with vertex functions as Hecke eigenfunctions.