Cyclic Representations of Quantum (Super) Algebras At q<SUP>p</SUP>=1

FU Hong-Chen; GE Mo-Lin

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2024年10月30日

Chinese Physics C> 1993, Vol. 17> Issue(8) : 700-709

Cyclic Representations of Quantum (Super) Algebras At q^p=1

FU Hong-Chen ^, ,
GE Mo-Lin

Theoretical Physics Division,Nankai Institute of Mathematics,Tianjin 300071

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Abstract：
Cyclic representations of quantum (super) algebras are studied at q^p=1 using two methods:the quotient module method and the q-boson realization method.For the quantum algebras associated with any finite dimensional simple Lie algebra the general theory of two methods is given,and is generated to the quantum superalgebra U_qosp(1.2).By constructing the cyclic representation of q-Heisenberg-Wey1 superalgebras the q-boson realization method is generated to construction of cyclic representations of some high-rank quantum superalgebras.

References

[1]

V. G. Drinfeld, Proc. ICM(Berkeley, 1986)，P798.[2]M. Jimbo, Lett. Math. Phys.，10(1985),63;11(1986),247.[3]N. Yu. Peshetikhin, LOMI Preprint E-4 and E-11(1987).[4]M. Rosso, Commun. Math. Phys.，10(1988),581，124(1989),307.[5]C. De. Concini, V. G. Kac, Representations of quantum groups at q roots of 1，Preprint 1990.[6]E. Date, M. Jimbo, K. Miki, T. Miwa, Preprint RIMS-703, RIMS-706.[7]C. P. Sun, M. L. Ge, "Cyclic q-deformed bosons and cyclic representations of quantum algebra sl(2)q",J.Phys. A, in press.[8]C. P. Sun, M. L. Ge, X. F. Liu, "Cyclic boson algebra and q-boson realization of cyclic representations of quantum algebra sl(3) q at qP=1, J. Phys. A, in press.[9]H. C. Fu, M. L. Ge, J. Math. Phys.，33(1992),427.[10]H. C. Fu, M. L. Ge,Conemun. Theor.Phys.，18(1992),373.[11]H. C. Fu, M. L. Ge, "Cyclic representation of the q-deformed Heisenberg-Weyl superalgebras and q-boson-fermion realization of cyclic representations of quantum superalgebra Uqsl(m,n) st qp=1",Commun. Theor.Phys.，in press.[12]C. P. Sun, H. C. Fu, M. L. Ge, Lett. Math. Phys.，23(1991),19.[13]N. Burroughs, Commus. Math. Phys.，127(1990),109.[14]L. C. Biedenharn, J. Phys.，A22(1989),L873.[15]A. J. Macfarlane, J. Phys.，A22(1989),4581.[16]C. P. Sun, H. C. Fu, J. Phys.，A22(1989),L983.[17]M. Chaichian, P. Kulish, J. Lukietski, Phys. Lett.，B237(1990),383.[18] R. Floreanini, V. P. Spiridonov, L. Vinet, Phys. Lett.，B242 (1990 ) , 383: Commun. Math. Phys.，137(1991),149.[19]M. Jimbo, Lecture Notes .Physics. No. 246, p335.

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FU Hong-Chen and GE Mo-Lin. Cyclic Representations of Quantum (Super) Algebras At q^p=1[J]. Chinese Physics C, 1993, 17(8): 700-709.

FU Hong-Chen and GE Mo-Lin. Cyclic Representations of Quantum (Super) Algebras At q^p=1[J]. Chinese Physics C, 1993, 17(8): 700-709. shu

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Received: 1900-01-01
Revised: 1900-01-01

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Cyclic Representations of Quantum (Super) Algebras At q^p=1

FU Hong-Chen ^,
GE Mo-Lin

Corresponding author: FU Hong-Chen,

Theoretical Physics Division,Nankai Institute of Mathematics,Tianjin 300071

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1993-08-05

Abstract: Cyclic representations of quantum (super) algebras are studied at q^p=1 using two methods:the quotient module method and the q-boson realization method.For the quantum algebras associated with any finite dimensional simple Lie algebra the general theory of two methods is given,and is generated to the quantum superalgebra U_qosp(1.2).By constructing the cyclic representation of q-Heisenberg-Wey1 superalgebras the q-boson realization method is generated to construction of cyclic representations of some high-rank quantum superalgebras.