302 citations · 1k across the 44 of their papers we have counts for
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Representations of the Heisenberg algebra by difference operators
Andrzej Z. Gorski, Jacek Szmigielski
We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence princ…
Principal Realization for the extended affine Lie algebra of type with coordinates in a simple quantum torus with two generators
Stephen Berman, Jacek Szmigielski
We construct an irreducible representation for the extended affine algebra of type with coordinates in a quantum torus. We explicitly give formulas using vertex operators si…
On Pairs of Difference Operators Satisfying: [P,Q] = Id
Andrzej Z. Gorski, Jacek Szmigielski
Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown…
On Soliton Content of Self Dual Yang-Mills Equations
Jacek Szmigielski
Exploiting the formulation of the Self Dual Yang-Mills equations as a Riemann-Hilbert factorization problem, we present a theory of pulling back soliton hierarchies to the Self Dua…