Abstract
Explicit recurrence formulas of canonical realization (boson representation) for quantum enveloping algebrasU q (gl(n, C)) are given. Using them, irreducible highest weight representations ofU q (gl(n, C)) are obtained as restriction of representation of Fock space to invariant subspace generated by vacuum as a cyclic vector.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Biedenharn, L.C.: The quantum groupSU q (2) and aq-analoque of the boson operators. J. Phys. A: Math. Gen.22, L873–878 (1989)
Macfarlane, A.J.: Onq-analogues of the quantum harmonic oscillator and the quantum groupSU q (2). J. Phys. A.: Math. Gen.22, 4581–4588 (1989)
Zurong, Yu.: A new method of determining an irreducible representationsl q (3) algebra (I). J. Phys. A.: Math. Gen.24, L399-L402 (1991)
Sun, Chang-Pu, Ge, Mo-Lin: Theq-analog of the boson algebra, its representation on the Fock space, and applications to the quantum group. J. Math. Phys.32, 595–598 (1991)
Rosso, M.: Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra. Commun. Math. Phys.117, 581–593 (1988)
Lusztig, G.: Quantum deformation of certain simple modules of enveloping algebras. Adv. Math.70, 237–249 (1988)
Jimbo, M.: Aq-analogue ofU(gl(n+1)), Hecke algebra and the Yang-Baxter equation. Lett. Math. Phys.11, 247–252 (1986)
Burdík, C.: Realizations of the semisimple Lie algebras: The method of construction, J. Phys. A: Math. Gen.18, 3101–3111 (1986)
Jimbo, M.: QuantumR-matrix related to the generalized Toda system: an algebraic approach. Lectures Notes in Physics, vol.246, pp. 335–361. Berlin, Heidelberg, New York: Springer 1985
Hayashi, T.:Q-analogues of Clifford and Weyl algebras — Spinor and oscillator representations of quantum enveloping algebras. Commun. Math. Phys.127, 129–144 (1990)
Sun, Chang-Pu, Fu, Hong-Chen: Theq-deformed boson realisations of the quantum groupsSU(n) and its representations. J. Phys. A.: Math. Gen22, L983-L986 (1989)
Burdík, C., Havlíček, M., Thoma, M: Finite-dimensional representations of the simple Lie algebras: Once more. An examplesl(3,C). Preprint Nucl. Centre, Charles University Prague, PRA-HEP-90/11
Havlíček, M., Lassner, W.: Canonical realizations of the Lie algebrasgl(n, R) andsl(n, R). I. Formulae and classification. Rep. Math. Phys.8, 391–399 (1976)
Exner, P., Havlíček, M., Lassner, W.: Canonical realizations of classical Lie algebras. Czech. J. Phys. B26, 1213–1225 (1976)
Havlíček, M., Exner, P.: Matrix canonical realizations of the Lie algebrao(m, n). Basic formulae and classification. Ann. Inst. H. Poinc.23, 335–347 (1975)
Havlíček, M., Lassner, W.: Canonical realizations of the Lie algebrasp(2n, R). Int. J. Theor. Phys.15, 867 (1977)
Havlíček, M., Lassner, W.: Matrix canonical relaizations of the Lie algebrau(p, q). Rep. Math. Phys.12, 1–8 (1977)
Arnaudon, D., Chakrabarti, A.: Periodic and partial periodic representations ofSU(N) q . Commum. Math. Phys.139, 461–478 (1991)
Author information
Authors and Affiliations
Additional information
Communicated by K. Gawedzki
Rights and permissions
About this article
Cite this article
Burdík, Č., Havlíček, M. & Vančura, A. Irreducible highest weight representations of quantum groupsU q (gl(n, C)). Commun.Math. Phys. 148, 417–423 (1992). https://doi.org/10.1007/BF02100869
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02100869