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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 onmixed dihedral braid relations between Demazure operators and simple reflections.
Palestine Journal of Mathematics
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 realise 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.
Theses:
Doctorate thesis 2025: Some monoidal and module categories in representation theory
In this thesis, we study several problems from monoidal representation theory. In the
first chapter we construct two diagrammatic categories – one monoidal and one module –
category in order to describe representations of a quantum symmetric pair. In the second
chapter we show that nil Hecke algebras form Hopf algebroids without antipodes via
mixed dihedral braid relations. In the third chapter we introduce duodule categories
over duoidal categories to provide a ring-theoretic framework for constructing free strict
module categories over strict monoidal categories.
Master's thesis 2022: 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.
Bachelor's thesis 2019: Idempotente und Jones-Wenzl Projektoren. (german)
This is worth reading if you want to discover the importance of idempotents in representation theory & learn about both idempotents in group algebras of symmetric groups (called Young symmetrizers) as well as their connection to idempotents in Temperley-Lieb algebras (called Jones-Wenzl projectors).
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