Lohe, M.Thilagam, A.2006-12-042006-12-042005Journal of Physics A: Mathematical and Theoretical, 2005; 38(2):461-4831751-81130305-4470http://hdl.handle.net/2440/17868Copyright © 2005 IOP PublishingWe develop algebraic properties of Weyl-ordered polynomials in the momentum and position operators P, Q which satisfy the R-deformed Heisenberg algebra, representations of which describe quantum mechanics in fractional dimensions. By viewing Weyl-ordered polynomials as tensor operators with respect to the Lie algebra sl₂(C) we derive a specific form for these polynomials, including an expression in terms of hypergeometric functions, and determine various algebraic properties such as recurrence relations, symmetries, and also a general product formula from which all commutators and anti-commutators may be calculated. We briefly discuss several applications to quantum mechanics in fractional dimensions.enJournal article002005004910.1088/0305-4470/38/2/0120002266311000142-s2.0-1194425512255338Lohe, M. [0000-0002-5214-2225]