Hermitian symmetric modular category O

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The case of a parabolic category O when the parabolic has an abelian unipotent radical, the so-called hermitian symmetric case, is special in that the Kazhdan-Lusztig-conjectures can be proven without using the decomposition theorem and the extensions between Verma modules are known. This gives hope that it should be possible to prove analogous statements in the modular case. Generalizing the modular Koszul duality recently established by the applicant in collaboration with Simon Riche and Geordie Williamson to a parabolic-singular duality, this should lead to new formulas for extensions of singular Weyl modules.