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Tilting sheaves for real groups and Koszul duality

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The theory of tilting sheaves facilitates geometric proofs for results in representation theory.
A fully faithful embedding links tilting sheaves to Soergel bimodules, enhancing our understanding of group actions.
This work directly supports previous conjectures regarding quasi-split groups and their structure theorems.
Real analogs of classical theories are established, providing a novel approach to studying real group actions.

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This research develops a theory of tilting sheaves for real groups, highlighting Koszul duality applications.

Ionov et al. (2025) studied this question.

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