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On the Finkelberg-Ginzburg Mirabolic Monodromy Conjecture

Valerio Toledano-LaredoRobin Walters
Dec 2022
摘要
We compute the monodromy of the mirabolic Harish-Chandra D-module for all butan explicit codimension two set of values of the parameters (theta,c). Inparticular, we show that the Finkelberg-Ginzburg conjecture, which is known tohold for generic values of the parameters, fails at special values even in rank1. Our main tools are Opdam's shift operators and normalised intertwiners forthe extended affine Weyl group, which allow for the resolution of resonancesoutside the codimension two set.
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