p a p e r s

2026

Infinite sequences via Lie algebra actions for oligomorphic groups

We define tensor powers in the setting of oligomorphic groups generalizing work of Entova-Aizenbud. We further define Lie algebra actions on such tensor powers utilizing Harman-Snowden measures for oligomorphic groups. In total we obtain a uniform framework for a unimodality argument of Stanley for finite integer sequences and a monotonicity argument of Cameron for infinite integer sequences. (ArXiv)

2025

A study of nil Hecke algebras via Hopf algebroids

Hopf algebroids are generalizations of Hopf algebras to less commutative settings.  We show how the comultiplication defined by Kostant and Kumar turns the affine nil Hecke algebra associated to a Coxeter system into a Hopf algebroid without an antipode. The proof relies on mixed dihedral braid relations between Demazure operators and simple reflections. (Palestine Journal of Mathematics, ArXiv)

Diagrammatics for the smallest quantum coideal and Jones-Wenzl projectors (with Catharina Stroppel)

We describe algebraically, diagrammatically and in terms of weight vectors, the restriction of tensor powers of the standard representation of quantum sl2 to a coideal subalgebra. We realize the category as module category over the monoidal category of type ±1 representations in terms of string diagrams and via generators and relations. The idempotents projecting onto the quantized eigenspaces are described as type B/D analogues of Jones--Wenzl projectors. As an application we introduce and give recursive formulas for analogues of Θ-networks. (Glasgow Mathematical Journal, ArXiv)

Master's thesis: Categorified Jones-Wenzl Projectors and Generalizations.

This thesis is topic wise a continuation/generalization of my Bachelor's thesis from type A to types B & D. Interesting aspects include the type B branching rule, type B Young symmetrizers, type D full twists. We extended the connection to the quantum symmetric pair in its own paper above. (ArXiv)