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

DOI10.1007/BF02101875zbMath0751.17006MaRDI QIDQ1180229

Daniel Arnaudon, Amithaba Chakrabarti

Publication date: 27 June 1992

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

representationsquantized enveloping algebrairreducible representationsGelfand-Zetlin basisperiodic representations

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)

Related Items

Roots of unity: Representations of quantum groups ⋮ On the universal \(R\)-matrix of \(U_ q\widehat{sl}_ 2\) at roots of unity ⋮ SO(5)q and contraction: Chevalley basis representations for q-generic and root of unity ⋮ The fundamental invariant of the Hecke algebra Hn(q) characterizes the representations of Hn(q), S n, SUq(N), and SU(N) ⋮ Irregular Uq (sl(3)) representations at roots of unity via Gel’fand–(Weyl)–Zetlin basis ⋮ Polynomial realization of the Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis ⋮ Flat periodic representations of \({\mathcal U}_ q({\mathcal G})\) ⋮ Normalized Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis and new summation formulas for q-hypergeometric functions ⋮ Irreducible highest weight representations of quantum groups \(U_ q(gl(n,\mathbb{C}{}))\) ⋮ Raising and lowering operators for U q (gl(n))

Cites Work

• Unnamed Item
• Quantum groups at roots of 1
• Irreducible representations of the quantum analogue of SU(2)
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Cyclic \(L\)-operator related with a 3-state \(R\)-matrix
• Generalized chiral Potts models and minimal cyclic representations of \(U_ q (\widehat {\mathfrak gl}(n,C))\)
• Gelfand-Zetlin basis for \(U_ q(\mathfrak{gl}(\text{\textbf{N}}+\text{\textbf{1}}))\) modules.
• Periodic and flat irreducible representations of \(SU(3)_ q\)
• Chiral Potts model as a descendant of the six-vertex model
• q-analogs of IU(n) and U(n,1)
• Operators that Lower or Raise the Irreducible Vector Spaces of U n−1 Contained in an Irreducible Vector Space of Un
• Class of Representations of the IU(n) and IO(n) Algebras and Respective Deformations to U(n, 1), O(n, 1)

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