Normalized Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis and new summation formulas for q-hypergeometric functions

DOI10.1063/1.1310360zbMath0971.81046OpenAlexW1973233645MaRDI QIDQ2738278

A. D. Mitov, Piero Truini, Vladimir K. Dobrev

Publication date: 30 August 2001

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

Full work available at URL: https://doi.org/10.1063/1.1310360

zbMATH Keywords

basic hypergeometric functionsquantum groupsholomorphic representationsGelfand-Weyl-Zeltin basis

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) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (5)

The multiple sum formulas for 12j coefficients of SU(2) and uq(2) ⋮ A functional realization of the Gelfand-Tsetlin base ⋮ Gelfand–Tsetlin Bases for Classical Lie Algebras ⋮ A Gelfand-Tsetlin-type basis for the algebra \(\mathfrak{sp}_4\) and hypergeometric functions ⋮ Construction of the Gelfand-Tsetlin basis for unitary principal series representations of the algebra \(sl_n(\mathbb{C})\)

Cites Work

• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Periodic and partially periodic representations of \(\text{SU}(N)_ q\)
• Flat periodic representations of \({\mathcal U}_ q({\mathcal G})\)
• An extension of the Borel-Weil construction to the quantum group \(U_ q(n)\)
• Gelfand-Zetlin basis for \(U_ q(\mathfrak{gl}(\text{\textbf{N}}+\text{\textbf{1}}))\) modules.
• On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra
• q-analogs of IU(n) and U(n,1)
• Complementarity of su_q(3) and u_q(2) and q-boson realization of the su_q(3) irreducible representations
• Representation theory approach to the polynomial solutions of q-difference equations: Uq(sl(3)) and beyond
• Polynomial realization of the Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis
• Raising and lowering operators for u_q(n)
• On the Representations of the Semisimple Lie Groups. II
• Class of Representations of the IU(n) and IO(n) Algebras and Respective Deformations to U(n, 1), O(n, 1)

This page was built for publication: Normalized Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis and new summation formulas for q-hypergeometric functions