Moment graphs in representation theory and geometry
Peter Fiebig
TL;DR
This paper reviews the use of moment graphs to convert representation theory problems into geometric ones, focusing on semisimple complex Lie algebras and their flag varieties.
Contribution
It demonstrates how Kazhdan-Lusztig conjecture problems can be reformulated as multiplicity problems for parity sheaves on flag varieties.
Findings
Translation of Kazhdan-Lusztig conjecture into geometric multiplicity problems
Application of moment graph techniques to representation theory
Focus on semisimple complex Lie algebras and flag varieties
Abstract
This paper reviews the moment graph technique that allows to translate certain representation theoretic problems into geometric ones. For simplicity we restrict ourselves to the case of semisimple complex Lie algebras. In particular, we show how the original Kazhdan-Lusztig conjecture on the characters of irreducible highest weight representations can be translated into a multiplicity problem for parity sheaves on the (Langlands dual) flag variety.
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