On Harder-Narasimhan filtrations and their compatibility with tensor\n products

Abstract

We attach buildings to modular lattices and use them to develop a metric\napproach to Harder-Narasimhan filtrations. Switching back to a categorical\nframework, we establish an abstract numerical criterion for the compatibility\nof these filtrations with tensor products. We finally verify our criterion in\nthree cases, one of which is new.\n