Periodic and partially periodic representations of \(\text{SU}(N)_ q\) (Q1180229)

The authors are concerned here with some special representations of the quantized enveloping algebra of type \(A_ n\), when the deformation parameter is a root of unity. They construct them using a quantum version of the so-called Gelfand-Zetlin basis. Alternatively, they introduce an auxiliary algebra, whose irreducible representations are in one-to-one correspondence with the irreducible periodic representations of \(U_ q(sl(n))\). See also the review below.