Split quaternionic analysis and separation of the series for \(\mathrm{SL}(2,\mathbb R)\) and \(\mathrm{SL}(2,\mathbb C)/\mathrm{SL}(2,\mathbb R)\)

DOI10.1016/j.aim.2011.06.001zbMath1264.30037arXiv1009.2532OpenAlexW1695974975MaRDI QIDQ639535

Matvei Libine, Igor B. Frenkel

Publication date: 22 September 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.2532

zbMATH Keywords

Minkowski spacerepresentation theorysplit quaternionsquaternion analysisLobachevski space

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Analysis on real and complex Lie groups (22E30)

Related Items (23)

Some similarities classes related to O(2,1) in split quaternions ⋮ On the roots of coquaternions ⋮ The conformal four-point integrals, magic identities and representations of \(U(2,2)\) ⋮ The Moore-Penrose inverses of split quaternions ⋮ Gleason's problem, rational functions and spaces of left-regular functions: the split-quaternion setting ⋮ The Moore-Penrose inverse and singular value decomposition of split quaternions ⋮ Clifford Algebras with Induced (Semi)-Riemannian Structures and Their Compactifications ⋮ Regular functions on the scaled hypercomplex numbers ⋮ Basins of attraction for a quadratic coquaternionic map ⋮ A survey of some recent results on Clifford algebras in \(\mathbb{R}^4\). ⋮ On complex split quaternion matrices ⋮ The regularity of functions on dual split quaternions in Clifford analysis ⋮ Quaternionic analysis, representation theory and physics ⋮ Unnamed Item ⋮ Clifford analysis with indefinite signature ⋮ Magic identities for the conformal four-point integrals; the Minkowski metric case ⋮ The Jacobi matrix for functions in noncommutative algebras ⋮ The Two-Loop Ladder Diagram and Representations of U(2,2) ⋮ Split-quaternionic Hermitian Clifford analysis ⋮ Regular functions on dual split quaternions in Clifford analysis ⋮ Projections Separating Spectra for $\boldsymbol{L^2}$ on Pseudounitary Groups $\boldsymbol{{\mathrm U}(p,q)}$ ⋮ n-Regular functions in quaternionic analysis ⋮ Split-quaternions and the Dirac equation

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