This quantity is dedicated to quite a number very important new rules coming up within the functions of Lie teams and Lie algebras to Schrödinger operators and linked quantum mechanical platforms. In those functions, the gang doesn't look as a average symmetry staff, yet really as a "hidden" symmetry workforce whose illustration concept can nonetheless be hired to investigate at least a part of the spectrum of the operator. In mild of the fast advancements during this topic, a unique consultation was once prepared on the AMS assembly at Southwest Missouri nation college in March 1992 which will compile, maybe for the 1st time, mathematicians and physicists operating in heavily similar parts. The contributions to this quantity hide Lie team tools, Lie algebras and Lie algebra cohomology, illustration thought, orthogonal polynomials, $q$-series, conformal box thought, quantum teams, scattering idea, classical invariant idea, and different subject matters. This quantity, which includes a very good stability of study and survey papers, provides a glance at a few of the present advancements during this terribly wealthy and brilliant quarter.
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