## Abstract

On the coordinate ring of GL_{q}(n), we show that the trace of _{q}X^{m}, the q-analogue of the mth power of Xε{lunate}GL_{q}(n), is represented by the polynomial of tr(_{q}X^{k}), 1≤k≤n-1, and det _{q}X for m≥n by using the quantum Cayley-Hamilton formula. This shows that, if one can take tr(_{q}X^{k}), k=1, 2, ..., as commutative Hamiltonians on the coordinate ring of GL_{q}(n), the number of algebraic independent Hamiltonians is finite. Furthermore we show that the first Hamiltonian tr(_{q}X) and the second Hamiltonian tr(_{q}X^{2}) commute with each other. We observe the q-analogue of the Toda molecule by using quantum group symmetry.

Original language | English |
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Pages (from-to) | 43-50 |

Number of pages | 8 |

Journal | Physics Letters A |

Volume | 183 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1993 Nov 29 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Physics and Astronomy

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