Algebraic dependence of Hamiltonians on the coordinate ring of the quantum group GLq(n)

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Abstract

On the coordinate ring of GLq(n), we show that the trace of qXm, the q-analogue of the mth power of Xε{lunate}GLq(n), is represented by the polynomial of tr(qXk), 1≤k≤n-1, and det qX for m≥n by using the quantum Cayley-Hamilton formula. This shows that, if one can take tr(qXk), k=1, 2, ..., as commutative Hamiltonians on the coordinate ring of GLq(n), the number of algebraic independent Hamiltonians is finite. Furthermore we show that the first Hamiltonian tr(qX) and the second Hamiltonian tr(qX2) commute with each other. We observe the q-analogue of the Toda molecule by using quantum group symmetry.

Original languageEnglish
Pages (from-to)43-50
Number of pages8
JournalPhysics Letters A
Volume183
Issue number1
DOIs
Publication statusPublished - 1993 Nov 29
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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