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

Research output: Contribution to journalArticle

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

Fingerprint

Toda Lattice
Partial Differential Operators
Radon Transform
Radon
Commutative Ring
Algebra
Integrability
Quantum Integrable Systems
Fourier Integral Operators
Completely Integrable Systems
Enveloping Algebra
Commutativity
Homomorphism
Ring
Invariant
Demonstrate

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Analysis

Cite this

The algebraic integrability of the quantum toda lattice and the radon transform. / Ikeda, Kaoru.

In: Journal of Fourier Analysis and Applications, Vol. 15, No. 1, 02.2009, p. 80-100.

Research output: Contribution to journalArticle

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