REVIEW 1 cited by
Temperley-Lieb, Brauer and Racah algebras and other centralizers of su(2)
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
In the spirit of the Schur-Weyl duality, we study the connections between the Racah algebra and the centralizers of tensor products of three (possibly different) irreducible representations of su(2). As a first step we show that the Racah algebra always surjects onto the centralizer. We then offer a conjecture regarding the description of the kernel of the map, which depends on the irreducible representations. If true, this conjecture would provide a presentation of the centralizer as a quotient of the Racah algebra. We prove this conjecture in several cases. In particular, while doing so, we explicitly obtain the Temperley-Lieb algebra, the Brauer algebra and the one-boundary Temperley-Lieb algebra as quotients of the Racah algebra.
Forward citations
Cited by 1 Pith paper
-
Revisiting the Askey--Wilson algebra with the universal R-matrix of $U_q(sl(2))$
A new R-matrix formula defines the third Askey-Wilson generator as a conjugate of the Casimir element in U_q(sl(2))^{⊗3}, and the Askey-Wilson relations are derived from it.
Discussion (0). Continue with ORCID to comment.