n-Regular functions in quaternionic analysis

DOI10.1142/S0129167X21500087zbMath1462.30096arXiv2011.14188OpenAlexW3116729880MaRDI QIDQ5856988

Matvei Libine, Igor B. Frenkel

Publication date: 30 March 2021

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.14188

zbMATH Keywords

conformal groupquaternionic regular functionsCauchy-Fueter formulasunitary representations of \(\operatorname{SU}(2,2)\)

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Functions of hypercomplex variables and generalized variables (30G35) Applications of Lie groups to the sciences; explicit representations (22E70)

Cites Work

• Split quaternionic analysis and separation of the series for \(\mathrm{SL}(2,\mathbb R)\) and \(\mathrm{SL}(2,\mathbb C)/\mathrm{SL}(2,\mathbb R)\)
• Quaternionic analysis, representation theory and physics
• Wave and Dirac operators, and representations of the conformal group
• Analysis on the minimal representation of O(\(p,\) \(q\)). III: Ultrahyperbolic equations on \(\mathbb{R}^{p-1,q-1}\)
• Comparative accuracy of averaged estimates of spectral density for continuous and discrete realizations
• On some degenerate principal series representations of \(U(n,n)\)
• Complexified clifford analysis
• Anti De Sitter Deformation of Quaternionic Analysis and the Second-Order Pole
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