Paritätsgarben auf Kashiwaras Fahnenmannigfaltigkeit

Drittmittelfinanzierte Gruppenförderung - Gesamtprojekt


Details zum Projekt

Projektleiter/in:
Prof. Dr. Peter Fiebig


Beteiligte FAU-Organisationseinheiten:
Professur für Mathematik

Mittelgeber: Deutscher Akademischer Austauschdienst (DAAD)
Projektstart: 01.09.2018
Projektende: 31.12.2019


Abstract (fachliche Beschreibung):

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. 


Externe Partner

University of Padova / Universita degli Studi di Padova

Zuletzt aktualisiert 2018-17-10 um 15:21