We show that each polynomial exponential functor on complex finite-dimensional
inner product spaces is defined up to equivalence of monoidal functors
by an involutive solution to the Yang–Baxter equation (an involutive
–matrix), which determines
an extremal character on
.
These characters are classified by Thoma parameters, and Thoma parameters resulting
from polynomial exponential functors are of a special kind. Moreover, we show that each
–matrix
with Thoma parameters of this kind yield a corresponding polynomial exponential
functor.
In the second part of the paper we use these functors to construct a higher twist
over for a
localisation of
–theory
that generalises the one classified by the basic gerbe. We compute the indecomposable part of
the rational characteristic classes of these twists in terms of the Thoma parameters of their
–matrices.
Keywords
twisted $K$–theory, polynomial functors, unit spectrum,
Fell bundles
