Erlangen Program at Large-2.5: Induced Representations and Hypercomplex Numbers - Mathematics > Representation TheoryReport as inadecuate




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Abstract: In the search for hypercomplex analytic functions on the half-plane, wereview the construction of induced representations of the group G=SL2,R.Firstly we note that G-action on the homogeneous space G-H, where H is anyone-dimensional subgroup of SL2,R, is a linear-fractional transformation onhypercomplex numbers. Thus we investigate various hypercomplex characters ofsubgroups H. The correspondence between the structure of the group SL2,R andhypercomplex numbers can be illustrated in many other situations as well. Wegive examples of induced representations of SL2,R on spaces of hypercomplexvalued functions, which are unitary in some sense. Raising-lowering operatorsfor various subgroup prompt hypercomplex coefficients as well.The paper contains both English and Russian versions.Keywords: induced representation, unitary representations, SL2,R,semisimple Lie group, complex numbers, dual numbers, double numbers, Moebiustransformations, split-complex numbers, parabolic numbers, hyperbolic numbers,raising-lowering operators, creation-annihilation operators



Author: Vladimir V. Kisil

Source: https://arxiv.org/



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