9 papers
Almost finitary birepresentation theory and applications to affine Soergel bimodules
Marco Mackaay, Vanessa Miemietz, Pedro Vaz
In this article, we develop a generalization of finitary birepresentation theory applicable to Soergel bimodules for infinite Coxeter groups. We establish a reduction process 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…
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…
Big data approach to Kazhdan-Lusztig polynomials
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
We investigate the structure of Kazhdan-Lusztig polynomials of the symmetric group by leveraging computational approaches from big data, including exploratory and topological data…
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…
Two-row Delta Springer varieties
Abel Lacabanne, Pedro Vaz, Arik Wilbert
We study the geometry and topology of -Springer varieties associated with two-row partitions. These varieties were introduced in recent work by Griffin-Levinson-Woo to give a ge…
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…
Odd Khovanov homology and higher representation theory
Léo Schelstraete, Pedro Vaz
We introduce a super analogue of -foams, and use it to define an invariant of oriented tangles, shown to coincide with odd Khovanov homology when restricted to lin…
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…