We study the tensor powers of the standard representation of the super-quantum algebra
, focusing
on the rings of its algebra endomorphisms, called centralizer algebras and denoted by
.
Their dimensions were conjectured by I Marin and E Wagner (Adv. Math. 248
(2013) 1332–1365). We prove this conjecture, describing the intertwiner spaces from a
semisimple decomposition as sets consisting of certain paths in a planar lattice with
integer coordinates. Using this model, we present a matrix unit basis for the centralizer
algebra
,
by means of closed curves in the plane, which are included in the lattice with integer
coordinates.
We have not been able to recognize your IP address
18.204.56.185
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.