# On the Cohomological Dimension of the Localization

```@inproceedings{Hecht1990OnTC,
title={On the Cohomological Dimension of the Localization},
author={Henryk Hecht and Dragan Mili{\vc}i{\'c}},
year={1990}
}```
• Published 1990
The left cohomological dimension of the localization functor is infinite for singular infinitesimal characters. Let g be a complex semisimple Lie algebra and X the flag variety of g, i. e. the variety of all Borel subalgebras in g. Let h be the (abstract) Cartan algebra of g, Σ the root system in h and Σ the set of positive roots determined by the condition that the homogeneous line bundles O(−μ) on X corresponding to dominant weights μ are positive. Denote by W the Weyl group of Σ. By a well… CONTINUE READING