John M. O'brien

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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.RT2018

Convolution Algebras for Finite Reductive Monoids

Jared Marx-Kuo, Vaughan McDonald, John M. O'Brien +1

For an arbitrary finite monoid $M$ and subgroup $K$ of the unit group of $M$ , we prove that there is a bijection between irreducible representations of $M$ with nontrivial $K$ -fixe…

math.RT2018

Characters of Renner Monoids and Their Hecke Algebras

Andy Hardt, Jared Marx-Kuo, Vaughan McDonald +2

This paper gives a general algorithm for computing the character table of any Renner monoid Hecke algebra, by adapting and generalizing techniques of Solomon used to study the rook…