Some homological properties of category O. IV
Representation Theory
2017-09-04 v1
Abstract
We study projective dimension and graded length of structural modules in parabolic-singular blocks of the BGG category O. Some of these are calculated explicitly, others are expressed in terms of two functions. We also obtain several partial results and estimates for these two functions and relate them to monotonicity properties for quasi-hereditary algebras. The results are then applied to study blocks of O in the context of Guichardet categories, in particular, we show that blocks of O are not always weakly Guichardet.
Keywords
Cite
@article{arxiv.1509.04391,
title = {Some homological properties of category O. IV},
author = {Kevin Coulembier and Volodymyr Mazorchuk},
journal= {arXiv preprint arXiv:1509.04391},
year = {2017}
}