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Maximal subalgebras in \({{\mathfrak {s}}}{{\mathfrak {o}}}(2,1)\), addition theorems and Bessel–Clifford functions

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Abstract

We consider some maximal nilpotent and maximal commutative subalgebras in \({{\mathfrak {s}}}{{\mathfrak {o}}}(2,1)\). The exponential mapping of these subalgebras gives the corresponding one-parameter subgroups. The relations between the corresponding bases of carrier space (which contain eigenfunctions of the infinitesimal operators of subrepresentations to the obtained subgroups) and kernels of some representation operators give some integral formulas for Bessel–Clifford functions. These relations are found to be particular cases of one continual addition theorem for the function introduced by authors.

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Authors and Affiliations

  1. Department of Higher Mathematics, National Research University MPEI, Krasnokazarmennaya 14, Moscow, 111250, Russia

    I. A. Shilin

  2. Department of Algebra, Moscow State Pedagogical University, Malaya Pirogovskaya 1, Moscow, 119991, Russia

    I. A. Shilin

  3. Department of Mathematics, Dongguk University, Gyeongju, 38066, Republic of Korea

    J. Choi

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  1. I. A. Shilin
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  2. J. Choi
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Correspondence to I. A. Shilin.

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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by I. A. Shilin and J. Choi. The first draft of the manuscript was written by I. A. Shilin and J. Choi commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Shilin, I.A., Choi, J. Maximal subalgebras in \({{\mathfrak {s}}}{{\mathfrak {o}}}(2,1)\), addition theorems and Bessel–Clifford functions. J Anal 31, 719–732 (2023). https://doi.org/10.1007/s41478-022-00435-9

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  • DOI: https://doi.org/10.1007/s41478-022-00435-9

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