Low interest rates lead to market concentration
Liu and al. argue that a reduction in long-term interest rates tends to make market structure less competitive within an industry. The reason is that while both the leader and follower within an industry increase their investment in response to a reduction in interest rates, the increase in investment is always stronger for the leader. As a result, the gap between the leader and follower increases as interest rates decline, making an industry less competitive and more concentrated.

Low Interest Rates, Market Power, and Productivity Growth
Authors: Ernest Liu, Atif Mian, Amir Sufi
From: Princeton University, University of Chicago
Market concentration leads to lower interest rates
Azar and Vives use an oligopolistic competition model to show that higher effective market concentration (including through common ownership) could potentially lead to lower equilibrium real interest rates.
Common Ownership and the Secular Stagnation Hypothesis
Authors: José Azar, Xavier Vives
From: University of Navarra, IESE Business School