Treffer: The multiple sum formulas for 12j coefficients of SU(2) and uq(2): The triple sum formulas for \(9j\) coefficients of SU(2) and \(\text{u}_q(2)\)

Title:
The multiple sum formulas for 12j coefficients of SU(2) and uq(2): The triple sum formulas for \(9j\) coefficients of SU(2) and \(\text{u}_q(2)\)
Authors:
Sigitas Ališauskas
Source:
Journal of Mathematical Physics. 43:1547-1568
Publication Status:
Preprint
Publisher Information:
AIP Publishing, 2000.
Publication Year:
2000
Subject Terms:
Quantum Physics, Generalized hypergeometric series, \({}_pF_q\), Other basic hypergeometric functions and integrals in several variables, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Connections of hypergeometric functions with groups and algebras, and related topics, Mathematical Physics (math-ph), 81R,33C,33D, Kampé de Fériet functions, Dougall's summation formula, 01 natural sciences, Finite-dimensional groups and algebras motivated by physics and their representations, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Chu-Vandermonde summation formulas, Mathematics - Quantum Algebra, 0103 physical sciences, FOS: Mathematics, Quantum Algebra (math.QA), hypergeometric \(_5\varphi_4\) series, 0101 mathematics, Wigner \(9j\) coefficients, Quantum Physics (quant-ph), Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Quantum groups and related algebraic methods applied to problems in quantum theory, Mathematical Physics
Document Type:
Fachzeitschrift Article<br />Other literature type
File Description:
application/xml
Language:
English
ISSN:
1089-7658
0022-2488
DOI:
10.1063/1.1436305
DOI:
10.1063/1.1312198
DOI:
10.48550/arxiv.math/9912142
Access URL:
http://arxiv.org/pdf/math/9912142
http://arxiv.org/abs/math/9912142
https://zbmath.org/1639428
https://doi.org/10.1063/1.1312198
https://arxiv.org/pdf/math/9912142
https://www.arxiv-vanity.com/papers/math/9912142/
https://arxiv.org/abs/math/9912142
https://aip.scitation.org/doi/10.1063/1.1312198
http://ui.adsabs.harvard.edu/abs/2000JMP....41.7589A/abstract
https://scitation.aip.org/content/aip/journal/jmp/41/11/10.1063/1.1312198
Rights:
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....2c0a5cb0c60eff187b7c48a9deb715e2
Database:
OpenAIRE

Weitere Informationen

The expressions for 12j coefficients of the both kinds (without and with braiding) of the SU(2) group and the quantum algebra uq(2) are considered. Using Dougall’s summation formula of the very well-poised hypergeometric F45(1) series and its q-generalization, several fourfold sum formulas [with each sum related to the balanced F45(1) or φ45 series] for the q-12j coefficients of the second kind (without braiding) are derived. Applying q-generalizations of rearrangement formulas of the very well-poised hypergeometric F56(−1) series [which correspond to a new expression for the Clebsch–Gordan coefficients of SU(2) and uq(2)], the new expressions with five sums [of the F34(1) and F23(1) or φ45 and φ23 type] are derived for the q-12j coefficients of the first kind (with braiding) instead of the usual expansions in terms of q-6j coefficients. Stretched and doubly stretched q-12j coefficients [as triple, double, or single sums, related to composed or separate hypergeometric F34(1) and F45(1) or φ33 and φ45 series and, particularly, to q-9j or q-6j coefficients] are considered.