Third Party Funds Group - Overall project
Start date : 01.09.2018
End date : 31.12.2019
Ziel des Projekts ist eine Beschreibung der Kategorie von Paritätsgarben auf einer koendlich stratifizierten Mannigfaltigkeit.
The project is located in pure mathematics and deals with a problem in geometric representation theory. Parity sheaves and moment graph techniques have proven to be extremely effective in answering questions in modular representation theory. In the finite-dimensional case a hypercohomology functor establishes a connection between parity sheaves and sheaves on moment graphs. However the geometry controlling representation theoretic phenomena in this case is often infinite-dimensional. We plan to study the category of parity sheaves on Kashiwara's infinite-dimensional thick-flag variety Y, to define a hypercohomology functor, to interpret its image as a category of moment graph sheaves and to establish an equivalence between parity sheaves and canonical sheaves on the moment graph. In a second phase, we intend to study base change and torsion phenomena in the category of parity sheaves on the thick flag manifold, in order to establish an equivalence between the category of projective objects in the category O of an affine Kac-Moody algebra at negative level and parity sheaves on Y.