arXiv subjects

Eric C Rowell

Publications and source records attributed to Eric C Rowell.

3 recordsLinked to original sources

arXiv2026

On Higher Representation Theory via Categories of type Charge-Conserving--with--Glue

In this paper we introduce a strict monoidal subcategory of the category of matrices, suitable to address a higher representation theoretic analogue of radicals (non-semisimplicity) in ordinary representation theory. We show the extent to which this analogue has analogous representation theoretic properties. To illustrate, we apply to two key problems in the study of braid representations (strict monoidal functors from the braid category $\mathsf{B}$ to the matrix category): the classification problem; and the problem of analysing the ordinary braid group representations that braid representations generate in towers.

math.QA↗

arXiv2024

Recovering R-symbols from modular data

Given a premodular category $\mathcal{C}$, we show that its $R$-symbol can be recovered from its $T$-matrice, fusion coefficients and some 2nd generalized Frobenius-Schur indicators. In particular, if $\mathcal{C}$ is modular, its $R$-symbols for a certain gauge choice are completely determined by its modular data.

math.QA↗

arXiv2022

Reconstruction of modular data from $SL_2(\mathbb{Z})$ representations

Modular data is the most significant invariant of a modular tensor category. We pursue an approach to the classification of modular data of modular tensor categories by building the modular $S$ and $T$ matrices directly from irreducible representations of $SL_2(\mathbb{Z}/n \mathbb{Z})$. We discover and collect many conditions on the $SL_2(\mathbb{Z}/n \mathbb{Z})$ representations to identify those that correspond to some modular data. To arrive at concrete matrices from representations, we also develop methods that allow us to select the proper basis of the $SL_2(\mathbb{Z}/n \mathbb{Z})$ representations so that they have the form of modular data. We apply this technique to the classification of rank-$6$ modular tensor categories, obtaining a classification up to modular data. Most of the calculations can be automated using a computer algebraic system, which can be employed to classify modular data of higher rank modular tensor categories.

math.QA↗