TY - JOUR
T1 - Algebraic dependence of Hamiltonians on the coordinate ring of the quantum group GLq(n)
AU - Ikeda, Kaoru
PY - 1993/11/29
Y1 - 1993/11/29
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=43949163312&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=43949163312&partnerID=8YFLogxK
U2 - 10.1016/0375-9601(93)90887-6
DO - 10.1016/0375-9601(93)90887-6
M3 - Article
AN - SCOPUS:43949163312
SN - 0375-9601
VL - 183
SP - 43
EP - 50
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 1
ER -