21 citations · 44 across the 15 of their papers we have counts for
20 papers
The dimension block of a spherical fusion category
Andrew Schopieray
Let be a spherical fusion category with global dimension . The Galois conjugates of the dimension character index a block of the -matrix of the Drinfeld center,…
On Haagerup-Izumi fusion categories
Terry Gannon, Andrew Schopieray, Harshit Yadav
For every odd , we construct a Haagerup-Izumi (HI) category for , using Barnes double-sine functions. Equivariantization gives near-group categories of type $((\mat…
Greedy fusion
Andrew Schopieray
We demonstrate that certain sequences of integer formal codegrees, motivated by the greedy algorithm for unit fraction decompositions of 1, dictate the structure of fusion rings. I…
Modular fusion categories with few twists
Andrew Schopieray
We classify modular fusion categories up to braided equivalence with less than four distinct twists of simple objects by observing that under this assumption, for each positive int…
Near-integral fusion
Jingcheng Dong, Andrew Schopieray
We abstract the study of irreducible characters of finite groups vanishing on all but two conjugacy classes, initiated by S. Gagola, to irreducible characters of fusion rings whose…
On Frobenius-Schur exponent bounds
Agustina Czenky, Julia Plavnik, Andrew Schopieray
Here we study bounds on the Frobenius-Schur exponent of spherical fusion categories based on their global dimension generalizing bounds from the representation theory of finite-dim…
Fixed-point-free fusion automorphisms
Andrew Schopieray
This is a study of fusion ring automorphisms leaving only the trivial element fixed. We prove that a variety of classical results on fixed-point-free automorphisms of finite groups…
Irrational braided generalized near-groups
Andrew Schopieray
We classify braided generalized near-group fusion categories whose global dimension is not an integer; there are exactly two up to Grothendieck equivalence and taking products with…
Categorification of integral group rings extended by one dimension
Andrew Schopieray
The integral group rings for finite groups are precisely those fusion rings whose basis elements have Frobenius-Perron dimension 1, and each is categorifiable in…
Modular tensor categories, subcategories, and Galois orbits
Julia Plavnik, Andrew Schopieray, Zhiqiang Yu +1
We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes a characterization of fusion su…
Nondegenerate extensions of near-group braided fusion categories
Andrew Schopieray
This is a study of weakly integral braided fusion categories with elementary fusion rules to determine which possess nondegenerately braided extensions of theoretically minimal dim…
Non-pseudounitary fusion
Andrew Schopieray
We prove there exist infinitely many inequivalent fusion categories whose Grothendieck rings do not admit any pseudounitary categorifications.
Norm, trace, and formal codegrees of fusion categories
Andrew Schopieray
We prove several results in the theory of fusion categories using the product (norm) and sum (trace) of Galois conjugates of formal codegrees. First, we prove that finitely-many fu…
Algebraic number fields generated by Frobenius-Perron dimensions in fusion rings
Terry Gannon, Andrew Schopieray
From a unifying lemma concerning fusion rings, we prove a collection of number-theoretic results about fusion, braided, and modular tensor categories. First, we prove that every fu…
Quadratic -numbers
Andrew Schopieray
Here we constructively classify quadratic -numbers: algebraic integers in quadratic number fields generating Galois-invariant ideals. We prove the subset thereof maximal among t…
Higher Gauss sums of modular categories
Siu-Hung Ng, Andrew Schopieray, Yilong Wang
The definitions of the Gauss sum and the associated central charge are introduced for premodular categories and . We first derive an…
Prime decomposition of modular tensor categories of local modules of Type D
Andrew Schopieray
Let be the unitary modular tensor categories arising from the representation theory of quantum groups at roots of unity for arbitrary simple finite-di…
Lie Theory for Fusion Categories: a Research Primer
Andrew Schopieray
A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions…
Level bounds for exceptional quantum subgroups in rank two
Andrew Schopieray
There is a long-standing belief that the modular tensor categories , for and finite-dimensional simple complex Lie algebras $\…
Classification of relations in the Witt group of nondegenerate braided fusion categories
Andrew Schopieray
The Witt group of nondegenerate braided fusion categories contains a subgroup consisting of Witt equivalence classes of pseudo-unitary nondege…