Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems

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Abstract

The integrable quantum many-body systems associated with the classical root systems are formulated in terms of the (trigonometric) Dunkl operators. We define the Dunkl operators by use of the infinite-dimensional representation of the R and K matrices for the Yang-Baxter equation and the reflection equation. The eigenvalues of systems are also given.

Original languageEnglish
Pages (from-to)394-401
Number of pages8
JournalJournal of the Physical Society of Japan
Volume65
Issue number2
DOIs
Publication statusPublished - 1996
Externally publishedYes

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many body problem
formalism
operators
eigenvalues
matrices

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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title = "Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems",
abstract = "The integrable quantum many-body systems associated with the classical root systems are formulated in terms of the (trigonometric) Dunkl operators. We define the Dunkl operators by use of the infinite-dimensional representation of the R and K matrices for the Yang-Baxter equation and the reflection equation. The eigenvalues of systems are also given.",
author = "Kazuhiro Hikami",
year = "1996",
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language = "English",
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AB - The integrable quantum many-body systems associated with the classical root systems are formulated in terms of the (trigonometric) Dunkl operators. We define the Dunkl operators by use of the infinite-dimensional representation of the R and K matrices for the Yang-Baxter equation and the reflection equation. The eigenvalues of systems are also given.

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