13 papers
Growth in affine Hecke categories
Kevin Coulembier, Jensen O'Sullivan, Daniel Tubbenhauer
This paper studies the asymptotic growth of tensor powers in affine Hecke categories, or equivalently of powers of Kazhdan--Lusztig basis elements in affine Hecke algebras. We prov…
Presentations for categories of crystals
Moaaz Alqady, David He, Daniel Tubbenhauer
We give generators and relations for the monoidal categories of crystals generated by the fundamental crystals of a simple complex Lie algebra. We also spell out several small-rank…
Affine diagram categories, algebras and monoids
David He, Daniel Tubbenhauer
We introduce and study several affine (=annular in this paper) versions of the classical diagram algebras such as Temperley-Lieb, partition, Brauer, Motzkin, rook Brauer, rook, pla…
Growth Problems of Quantum Groups
Jensen O'Sullivan, Daniel Tubbenhauer
We study the asymptotic size of decompositions of tensor powers of tilting modules for quantum groups (mostly at a complex root of unity). In type A1 we obtain a sharp result for t…
On detection probabilities of link invariants
Tuomas Kelomäki, Abel Lacabanne, Daniel Tubbenhauer +2
We prove that, for many standard link invariants, both the proportion of distinct invariant values and the detection probability among prime alternating links with at most n crossi…
Tensor powers of representations of (diagram) monoids
David He, Daniel Tubbenhauer
We study tensor powers of representations of finite monoids, focusing on the growth behavior of their composition length and the number of indecomposable summands. Special attentio…