Title: The spin-Brauer diagram algebra,
Abstract: We investigate the spin-Brauer diagram algebra, denoted ${\bf SB}_n(\delta)$,
that arises from studying an analogous form of Schur-Weyl duality for the
action of the pin group on ${\bf V}^{\otimes n} \otimes \Delta$. Here ${\bf V}$
is the standard $N$-dimensional complex representation of ${\bf Pin}(N)$ and
$\Delta$ is the spin representation. When $\delta = N$ is a positive integer,
we define a surjective map ${\bf SB}_n(N) \twoheadrightarrow {\rm End}_{{\bf
Pin}(N)}({\bf V}^{\otimes n} \otimes \Delta)$ and show it is an isomorphism for
$N \geq 2n$. We show ${\bf SB}_n(\delta)$ is a cellular algebra and use
cellularity to characterize its irreducible representations.