Commutative integrability of the full quantum Toda system (Q2722120)
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scientific article; zbMATH DE number 1617368
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Commutative integrability of the full quantum Toda system |
scientific article; zbMATH DE number 1617368 |
Statements
11 July 2001
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integrable system
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quantization
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universal enveloping algebra
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Toda system
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Commutative integrability of the full quantum Toda system (English)
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The author proves quantum integrability of the full Kostant-Toda system corresponding to a classical simple Lie algebra \(\mathfrak g\). This means commutation of the operators which are quantum counterparts of commuting (with respect to the Lie-Poisson brackets) integrals of the classical Toda system on the generic co-adjoint orbits of the Borel subgroup. Some commutative subalgebras of the universal enveloping algebras of \(\mathfrak g\) and its maximal nilpotent subalgebra are found.
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