Hermitian symmetric modular category O

当抛物线有一个阿贝尔单幂根时，即所谓的厄米对称情况，其特殊之处是kazhdan - lusztig猜想可以不使用分解定理证明，并且已知Verma模之间的扩展。这给了我们在模情况下证明类似命题的希望。将最近由申请人与Simon Riche和Geordie Williamson合作建立的模Koszul对偶推广到抛物-奇异对偶，这将导致奇异Weyl模扩展的新公式。

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.