From the 1 of 7 linked papers with an AI index.
7 papers
Big data approach to Kazhdan-Lusztig polynomials
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
The paper uses large‑scale computational and data‑analysis techniques to study Kazhdan‑Lusztig polynomials for symmetric groups up to size 11, revealing structural patterns through…
On Hecke and asymptotic categories for a family of complex reflection groups
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
Generalizing the dihedral picture for G(M,M,2), we construct Hecke algebras (and present a strategy for constructing Hecke categories) and asymptotic counterparts. We think of thes…
Asymptotics in infinite monoidal categories
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
We discuss formulas for the asymptotic growth rate of the number of summands in tensor powers in certain (finite or infinite) monoidal categories. Our focus is on monoidal categori…
On detection probabilities of link invariants
Tuomas Kelomäki, Tuomas Kelomäki, Abel Lacabanne +3
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…
Verma Howe duality and LKB representations
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
We establish a version of Howe duality that involves a tensor product of Verma modules. Surprisingly, this duality leaves the realm of lowest and highest weight modules. We quantiz…
A basis and Schur-Weyl duality for the loop Hecke algebra
Geoffrey Janssens, Abel Lacabanne, Léo Schelstraete +1
The loop Hecke algebra is a generalization of the Hecke algebra to the loop braid group, introduced by Damiani, Martin and Rowell. We give a new presentation of the loop Hecke alge…