Eric C. Rowell

EXTRASPECIAL 2-GROUPS AND IMAGES OF BRAID GROUP REPRESENTATIONS

We investigate a family of (reducible) representations of the braid groups Bn corresponding to a specific solution to the Yang‐Baxter equation. The images of Bn under these representations are finite groups, and we identify them precisely as extensions of extra-special 2-groups. The decompositions of the representations into their irreducible constituents are determined, which allows us to relate them to the well-known Jones representations of Bn factoring over Temperley‐Lieb algebras and the corresponding link invariants.

The N-eigenvalue problem and two applications

We consider the classification problem for compact Lie groups

Rank-finiteness for modular categories

G\subset U(n)

An algebra-level version of a link-polynomial identity of Lickorish

which are generated by a single conjugacy class with a fixed number

On a family of non-unitarizable ribbon categories

N

Unitarizability of premodular categories

of distinct eigenvalues. We give an explicit classification when N=3, and apply this to extract information about Galois representations and braid group representations.

Fermionic modular categories and the 16-fold way

We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are only finitely many modular categories of any fixed rank. Our technical advance is a generalization of the Cauchy theorem in group theory to the context of spherical fusion categories. For a modular category

Braid representations from unitary braided vector spaces

\mathcal{C}

Local representations of the loop braid group

with

Modular categories, integrality and Egyptian fractions

N=ord(T)