## Duke Mathematical Journal

### Compatibility of $t$-structures for quantum symplectic resolutions

#### Abstract

Let $W$ be a smooth complex variety with the action of a connected reductive group $G$. Adapting Teleman’s stratification approach to a microlocal context, we prove a vanishing theorem for the functor of $G$-invariant sections—that is, of quantum Hamiltonian reduction—for $G$-equivariant twisted $\mathcal{D}$-modules on $W$. As a consequence, when $W$ is affine we establish a sufficient combinatorial condition for exactness of the global sections functors of microlocalization theory. When combined with the derived equivalence results of our recent work, this gives precise criteria for “microlocalization of representation categories” in the spirit of Kashiwara–Rouquier and many other authors.

#### Article information

Source
Duke Math. J., Volume 165, Number 13 (2016), 2529-2585.

Dates
Revised: 16 October 2015
First available in Project Euclid: 23 June 2016

https://projecteuclid.org/euclid.dmj/1466703957

Digital Object Identifier
doi:10.1215/00127094-3619684

Mathematical Reviews number (MathSciNet)
MR3546968

Zentralblatt MATH identifier
06650078

#### Citation

McGerty, Kevin; Nevins, Thomas. Compatibility of $t$ -structures for quantum symplectic resolutions. Duke Math. J. 165 (2016), no. 13, 2529--2585. doi:10.1215/00127094-3619684. https://projecteuclid.org/euclid.dmj/1466703957

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