The \(6j\)-symbols for the \(SL(2,\mathbb{C})\) group

DOI10.1134/S0040577919010033zbMath1419.81020arXiv1711.07073OpenAlexW2936417955MaRDI QIDQ2313818

Sergey E. Derkachov, Vyacheslav P. Spiridonov

Publication date: 23 July 2019

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.07073

zbMATH Keywords

hypergeometric integral\(\operatorname{SL}(2,\mathbb{C})\) group

Mathematics Subject Classification ID

Spaces of operators; tensor products; approximation properties (46B28) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Unitary representations of locally compact groups (22D10) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Applications of group representations to physics and other areas of science (20C35)

Related Items (13)

An analog of the Dougall formula and of the de Branges-Wilson integral ⋮ Mellin-Barnes transformation for two-loop master-diagram ⋮ Tug-the-hook symmetry for quantum 6j-symbols ⋮ A constructive solution to the cosmological bootstrap ⋮ Racah coefficients for the group \(\operatorname{SL}(2,\mathbb{R} )\) ⋮ Classical \(6j\)-symbols of finite-dimensional representations of the algebra \(\mathfrak{gl}_3\) ⋮ Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles ⋮ Barnes-Ismagilov integrals and hypergeometric functions of the complex field ⋮ The endless beta integrals ⋮ Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group ⋮ Completeness of the \(3j\)-symbols for the group \(\mathrm{SL}(2, \mathbb{C} )\) ⋮ A pair of commuting hypergeometric operators on the complex plane and bispectrality ⋮ SOS-representation for the \(\operatorname{SL}(2,\mathbb{C})\)-invariant \(R\)-operator and Feynman diagrams

Cites Work

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• Self-dual continuous series of representations for \(\mathcal U_q(sl(2))\) and \(\mathcal U_q(osp(1|2))\)
• From principal series to finite-dimensional solutions of the Yang-Baxter equation
• On Racah operators
• Infinite conformal symmetry in two-dimensional quantum field theory
• Wilson function transforms related to Racah coefficients
• Racah operators for principal series of representations of the group $ \mathrm {SL}(2,\mathbb C)$
• General solution of the Yang–Baxter equation with symmetry group $\mathrm {SL}(\mathit {n},\mathbb {C})$
• Essays on the theory of elliptic hypergeometric functions
• Spin chains and Gustafson’s integrals
• Gustafson integrals for $SL(2, \mathbb{C})$ spin magnet
• Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of \(\mathcal U_q(\mathfrak{sl}(2,\mathbb R))\)

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