This quantity is dedicated to various vital new rules bobbing up within the functions of Lie teams and Lie algebras to Schrödinger operators and linked quantum mechanical platforms. In those purposes, the crowd doesn't look as a ordinary symmetry crew, yet relatively as a "hidden" symmetry staff whose illustration conception can nonetheless be hired to investigate at least a part of the spectrum of the operator. In mild of the quick advancements during this topic, a unique consultation used to be prepared on the AMS assembly at Southwest Missouri country collage in March 1992 with a purpose to assemble, might be for the 1st time, mathematicians and physicists operating in heavily comparable parts. The contributions to this quantity conceal Lie team tools, Lie algebras and Lie algebra cohomology, illustration concept, orthogonal polynomials, $q$-series, conformal box thought, quantum teams, scattering concept, classical invariant thought, and different issues. This quantity, which incorporates a great stability of study and survey papers, provides a glance at a few of the present advancements during this terribly wealthy and bright region.
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