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$\mathbf {Z}/m$-graded Lie algebras and perverse sheaves, IV


Authors: George Lusztig and Zhiwei Yun
Journal: Represent. Theory 24 (2020), 360-396
MSC (2010): Primary 22E60
DOI: https://doi.org/10.1090/ert/546
Published electronically: August 26, 2020
MathSciNet review: 4139898
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Abstract: Let $G$ be a reductive group over $\mathbf {C}$. Assume that the Lie algebra $\frak g$ of $G$ has a given grading $(\frak g_j)$ indexed by a cyclic group $\mathbf {Z}/m$ such that $\frak g_0$ contains a Cartan subalgebra of $\frak g$. The subgroup $G_0$ of $G$ corresponding to $\frak g_0$ acts on the variety of nilpotent elements in $\frak g_1$ with finitely many orbits. We are interested in computing the local intersection cohomology of closures of these orbits with coefficients in irreducible $G_0$-equivariant local systems in the case of the principal block. We show that these can be computed by a purely combinatorial algorithm.


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Additional Information

George Lusztig
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID: 117100
Email: gyuri@mit.edu

Zhiwei Yun
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID: 862829
Email: zyun@mit.edu

Received by editor(s): August 1, 2019
Received by editor(s) in revised form: June 24, 2020
Published electronically: August 26, 2020
Additional Notes: The first author was supported in part by NSF grant DMS-1855773.
The second author was supported in part by the Packard Foundation.
Article copyright: © Copyright 2020 American Mathematical Society