N M Atakishiyev and A U Klimyk 2002 J. Phys. A: Math. Gen. 35 5267 doi:10.1088/0305-4470/35/25/308
Diagonalization of operators and one-parameter families of nonstandard bases for representations of suq(2)
N M Atakishiyev1 and A U Klimyk2
Show affiliationsNonstandard bases for finite dimensional irreducible representations of the quantum algebra suq(2) are constructed by diagonalizing one-parameter families of the operators qJ3/4(J+ + J−)qJ3/4 + cqJ3 and iqJ3/4(J+ − J−)qJ3/4 + cqJ3, c 
. We derive explicit expressions for the eigenfunctions and the corresponding eigenvalues of these operators in an arbitrary irreducible representation of suq(2). It is shown that the matrix elements of the intertwining operator Aj(c), which is a q-extension of the classical su(2)-operator aj, J1aj = ajJ3, are expressed in terms of the dual q-Krawtchouk polynomials. Diagonalization of some other operators, associated with the dual q-Hahn polynomials, is also examined.
- PACS
- MSC
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81R15 Operator algebra methods (See also 46Lxx, 81T05)
81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
- Subjects
- Dates
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Issue 25 (28 June 2002)
Received 10 December 2001, in final form 25 April 2002
Published 14 June 2002
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Diagonalization of operators and one-parameter families of nonstandard bases for representations of suq(2)
N M Atakishiyev and A U Klimyk 2002 J. Phys. A: Math. Gen. 35 5267
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