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

Kaoru Ikeda

doi:10.1007/s00041-008-9048-7

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

Kaoru Ikeda

Faculty of Economics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	80-100
Number of pages	21
Journal	Journal of Fourier Analysis and Applications
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/s00041-008-9048-7
Publication status	Published - 2009 Feb 1

Keywords

Algebraic integrability
Quantum completely integrable systems
Radon transform
Toda lattice

ASJC Scopus subject areas

Analysis
Mathematics(all)
Applied Mathematics

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