John M. O'brien

collaborators

2 papers

math.RT2024

Lorentzian and Octonionic Satake equivalence

Tsao-Hsien Chen, John O'Brien

We establish a derived geometric Satake equivalence for the real group $G_{R} = P S O (2 n - 1, 1)$ (resp. $P E_{6} (F_{4})$ ), to be called the Lorentzian Satake equivalence (resp. Octoni…

math.RT2024

Homology of loops on a splitting-rank symmetric space via the Geometric Satake for real groups

John O'Brien

Using Nadler's Geometric Satake Equivalence for real reductive groups, we obtain a description of the equivariant homology of the loop space of splitting-rank symmetric spaces in t…