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Quasi-exactly-solvable spectral problems and conformal field theory. (English) Zbl 0805.58065
Kamran, Niky (ed.) et al., Lie algebras, cohomology, and new applications to quantum mechanics. AMS special session on Lie algebras, cohomology, and new applications to quantum mechanics, March 20-21, 1992, Southwest Missouri State University, Springfield, MO, USA. Providence, RI: American Mathematical Society. Contemp. Math. 160, 237-262 (1994).
Summary: We discuss recent progress in quasi-exactly solvable spectral problems. A few attempts of extending this method beyond the known algebraic structure are briefly reviewed. Remarkable parallels between the quasi- exactly solvable problems and conformal field theory in two dimensions is a new rapidly developing direction in this field which we dwell upon in the second half of this talk.
For the entire collection see [Zbl 0793.00019].

58Z05 Applications of global analysis to the sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
17B81 Applications of Lie (super)algebras to physics, etc.