2001/10/02 by Ewa Gnatowska, Gnatowska, Ewa, Aleksander Strasburger +1
Mathematics · Physics and Astronomy · #33C45 #33C55 #33C80 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 81R10 #Representation Theory (math.RT) #Secondary: 16W25 #math-ph #math.MP #math.RT #msc:16W25 #msc:33C45 #msc:33C55 #msc:33C80 #msc:81R10
paper · pdf · doi:10.48550/arxiv.math-ph/0110006
13 pages, uses bcp01e.sty
arxiv created 2001/10/02 · arxiv updated 2009/11/30
In this article we apply the duality technique of R. Howe to study the structure of the Weyl algebra. We introduce a one-parameter family of ``ordering maps'', where by an ordering map we understand a vector space isomorphism of the polynomial algebra on \NR2d with the Weyl algebra generated by creation and annihilation operators a1, ..., ad, a1+, ..., ad+. Corresponding to these orderings, we construct a one-parameter family of \fr sl2 actions on the Weyl algebra, what enables us to define and study certain subspaces of the Weyl algebra -- the space of Weyl spherical harmonics and the space of ``radial polynomials''. For the latter we generalize results of Luck and Biedenharn, Bender et al., and Koornwinder describing the radial elements in terms of continuous Hahn polynomials of the number operator.