%0 Generic %1 gannon2022classification %A Gannon, Tom %D 2022 %K D affine modules %T Classification of nondegenerate $G$-categories %U http://arxiv.org/abs/2206.11247 %X We classify a "dense open" subset of categories with an action of a reductive group, which we call nondegenerate categories, entirely in terms of the root datum of the group. As an application of our methods, we also: (1) Upgrade an equivalence of Ginzburg and Lonergan, which identifies the category of bi-Whittaker $D$-modules on a reductive group with the category of $W$-equivariant sheaves on a dual Cartan subalgebra $t^*$ which descend to the coarse quotient $t^*//W$, to a monoidal equivalence (where $W$ denotes the extended affine Weyl group) and (2) Show the parabolic restriction of a very central sheaf acquires a Weyl group equivariant structure such that the associated equivariant sheaf descends to the coarse quotient $t^*//W$, providing evidence for a conjecture of Ben-Zvi-Gunningham on parabolic restriction.

@misc{gannon2022classification, abstract = {We classify a "dense open" subset of categories with an action of a reductive group, which we call nondegenerate categories, entirely in terms of the root datum of the group. As an application of our methods, we also: (1) Upgrade an equivalence of Ginzburg and Lonergan, which identifies the category of bi-Whittaker $\mathcal{D}$-modules on a reductive group with the category of $\tilde{W}$-equivariant sheaves on a dual Cartan subalgebra $\mathfrak{t}^*$ which descend to the coarse quotient $\mathfrak{t}^*//\tilde{W}$, to a monoidal equivalence (where $\tilde{W}$ denotes the extended affine Weyl group) and (2) Show the parabolic restriction of a very central sheaf acquires a Weyl group equivariant structure such that the associated equivariant sheaf descends to the coarse quotient $\mathfrak{t}^*//\tilde{W}$, providing evidence for a conjecture of Ben-Zvi-Gunningham on parabolic restriction.}, added-at = {2022-06-23T08:44:42.000+0200}, author = {Gannon, Tom}, biburl = {https://www.bibsonomy.org/bibtex/2f710dcb13feb0455dbb5e29913dc439d/dragosf}, description = {Classification of nondegenerate $G$-categories}, interhash = {f63045531527966b0f2aacf5d537383c}, intrahash = {f710dcb13feb0455dbb5e29913dc439d}, keywords = {D affine modules}, note = {cite arxiv:2206.11247}, timestamp = {2022-06-23T08:44:42.000+0200}, title = {Classification of nondegenerate $G$-categories}, url = {http://arxiv.org/abs/2206.11247}, year = 2022 }