Periodic and partially periodic representations of \(\text{SU}(N)_ q\). (English) Zbl 0751.17006
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.
Reviewer: N.Andruskiewitsch (Bonn)
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
Keywords:
irreducible representations; quantized enveloping algebra; Gelfand-Zetlin basis; periodic representations; representationsCitations:
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