The spinor representations of the rotation group in a six-dimensional space with indefinite
metric are shown to be four-component spinors, which become the usual Dirac spinors …

Unitary equivariance is a natural symmetry that occurs in many contexts in physics and
mathematics. Optimization problems with such symmetry can often be formulated as …

We introduce some Z-graded versions of the walled Brauer algebra Br, s (δ), working over a
field of characteristic zero. This allows us to prove that Br, s (δ) is Morita equivalent to an …

In this paper, we provide the first efficient algorithm for port-based teleportation, a unitarily
equivariant version of teleportation useful for constructing programmable quantum …

Recently P. Deligne introduced the tensor category Rep (S_t)(for t not necessarily an
integer) which in a certain precise sense interpolates the categories Rep (S_d) of …

We classify indecomposable summands of mixed tensor powers of the natural
representation for the general linear supergroup up to isomorphism. We also give a formula …

We study representation theory of the partially transposed permutation matrix algebra, a
matrix representation of the diagrammatic walled Brauer algebra. This algebra plays a …

In this manuscript we analyse generalised port-based teleportation (PBT) schemes, allowing
for transmitting more than one unknown quantum state (or a composite quantum state) in …

This is the first in a series of papers in which we study representations of the Brauer category
and its allies. We define a general notion of triangular category that abstracts key properties …

This is an expanded version of the notes by the second author of the lectures on symmetric
tensor categories given by the first author at Ohio State University in March 2019 and later at …