ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The aim of this paper is to study q-harmonic polynomials on the quantum vector space generated by q-commuting elements x1,x2,...,xn. They are defined as solutions of the equation Δqp=0, where p is a polynomial in x1,x2,...,xn and the q-Laplace operator Δq is determined in terms of q-derivatives. The projector Hm:Am→Hm is constructed, where Am and Hm are the spaces of homogeneous (of degree m) polynomials and q-harmonic polynomials, respectively. By using these projectors, a q-analog of classical associated spherical harmonics is constructed. They constitute an orthonormal basis of Hm. A q-analog of separation of variables is given. Representations of the nonstandard q-deformed algebra Uq′(son) [which plays the role of the rotation group SO(n) in the case of classical harmonic polynomials] on the spaces Hm are explicitly constructed. © 2001 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1343092
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