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Abstract: This paper is an introduction to the use of perverse sheaves with positivecharacteristic coefficients in modular representation theory. In the firstpart, we survey results relating singularities in finite and affine Schubertvarieties and nilpotent cones to modular representations of reductive groupsand their Weyl groups. The second part is a brief introduction to the theory ofperverse sheaves with an emphasis on the case of positive characteristic andintegral coefficients. In the final part, we provide some explicit examples ofstalks of intersection cohomology complexes with integral or positivecharacteristic coefficients in nilpotent cones, mostly in type $A$. Some ofthese computations might be new.



Author: Daniel Juteau LMNO, Carl Mautner, Geordie Williamson

Source: https://arxiv.org/







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