Kisil, VV orcid.org/0000-0002-6593-6147 (2013) Induced Representations and Hypercomplex Numbers. Advances in Applied Clifford Algebras, 23 (2). pp. 417-440. ISSN 0188-7009
Abstract
In the search for hypercomplex analytic functions on the half-plane, we review the construction of induced representations of the group G=SL(2,R). Firstly we note that G-action on the homogeneous space G/H, where H is any one-dimensional subgroup of SL(2,R), is a linear-fractional transformation on hypercomplex numbers. Thus we investigate various hypercomplex characters of subgroups H. The correspondence between the structure of the group SL(2,R) and hypercomplex numbers can be illustrated in many other situations as well. We give examples of induced representations of SL(2,R) on spaces of hypercomplex valued functions, which are unitary in some sense. Raising/lowering operators for various subgroup prompt hypercomplex coefficients as well.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2012 Springer Basel. This is an author produced version of a paper published in Advances in Applied Clifford Algebras. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Induced representation; unitary representations; SL2(R); semisimple Lie group; complex numbers; dual numbers; double numbers; Möbius transformations; split-complex numbers; parabolic numbers; hyperbolic numbers; raising/lowering operators; creation/annihilation operators |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 08 Sep 2017 13:13 |
Last Modified: | 16 Jan 2018 16:55 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00006-012-0373-1 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111312 |