The algebraic integrability of the quantum toda lattice and the radon transform

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Abstract

We study the maximal commutative ring of partial differential operators which includes the quantum completely integrable system defined by the quantum Toda lattice. Kostant shows that the image of the generalized Harish-Chandra homomorphism of the center of the enveloping algebra is commutative (Kostant in Invent. Math. 48:101-184, 1978). We demonstrate the commutativity of the ring of partial differential operators whose principal symbols are N-invariant. Our commutative ring includes the commutative system of Kostant (Invent. Math. 48:101-184, 1978). The main tools in this paper are Fourier integral operators and Radon transforms.

Original languageEnglish
Pages (from-to)80-100
Number of pages21
JournalJournal of Fourier Analysis and Applications
Volume15
Issue number1
DOIs
Publication statusPublished - 2009 Feb 1

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Keywords

  • Algebraic integrability
  • Quantum completely integrable systems
  • Radon transform
  • Toda lattice

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

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