51 citations · 67 across the 22 of their papers we have counts for
23 papers
Torsion proliferation
Joseph Baine, Daniel Tubbenhauer
This paper considers the generic behaviour of sheaves supported on Schubert varieties in finite flag varieties. Our main results are that, for any fixed prime , as the rank of t…
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…
Idempotents, traces, and dimensions in Hecke categories
Ben Elias, Liam Rogel, Daniel Tubbenhauer
We explain how to compute idempotents that correspond to the indecomposable objects in the Hecke category. Closed formulas are provided for some common coefficients that appear in…
Quantum topology without topology
Daniel Tubbenhauer
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bri…
Growth Problems for Representations of Finite Monoids
David He, Daniel Tubbenhauer
We give a conjecture for the asymptotic growth rate of the number of indecomposable summands in the tensor powers of representations of finite monoids, expressing it in terms of th…
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…
Fractal behavior of tensor powers of the two dimensional space in prime characteristic
Kevin Coulembier, Pavel Etingof, Victor Ostrik +1
We study the number of indecomposable summands in tensor powers of the vector representation of SL2. Our main focus is on positive characteristic where this sequence of numbers and…
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…
Asymptotics in finite monoidal categories
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and re…
On rank one 2-representations of web categories
Daniel Tubbenhauer
We classify rank one 2-representations of SL2, GL2 and SO3 web categories. The classification is inspired by similar results about quantum groups, given by reducing the problem to…
Growth rates of the number of indecomposable summands in tensor powers
Kevin Coulembier, Victor Ostrik, Daniel Tubbenhauer
In this paper we study the asymptotic behavior of the number of summands in tensor products of finite dimensional representations of affine (semi)group (super)schemes and related o…
A formula to evaluate type A webs and link polynomials
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
We give a closed formula to evaluate exterior webs (also called MOY webs) and the associated Reshetikhin-Turaev link polynomials.
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…
Annular webs and Levi subalgebras
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
For any Levi subalgebra of the form we construct a quotient of the category of…
Minimal presentations of gln-web categories
Genta Latifi, Daniel Tubbenhauer
In this paper we study categories of gln-webs which describe associated representation categories of the quantum group Uq(gln). We give a minimal presentation of the category of gl…
Handlebody diagram algebras
Daniel Tubbenhauer, Pedro Vaz
In this paper we study handlebody versions of some classical diagram algebras, most prominently, handlebody versions of Temperley-Lieb, blob, Brauer, BMW, Hecke and Ariki-Koike alg…
Super -Howe duality and web categories
Daniel Tubbenhauer, Pedro Vaz, Paul Wedrich
We use super -Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of -modules (and, more generally…