Algebraic curves for commuting elements in the q-deformed Heisenberg algebra
arXiv:0710.2748 · doi:10.1016/j.jalgebra.2008.10.021
Abstract
In this paper we extend the eliminant construction of Burchnall and Chaundy for commuting differential operators in the Heisenberg algebra to the q-deformed Heisenberg algebra and show that it again provides annihilating curves for commuting elements, provided q satisfies a natural condition. As a side result we obtain estimates on the dimensions of the eigenspaces of elements of this algebra in its faithful module of Laurent series.
18 pages, 2 figures, LaTeX. Final version with some improvements in presentation. To appear in Journal of Algebra.