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The Harish-Chandra theorem for the quantum algebrau q (sl (3))

Abstract

A basis of a quantum universal enveloping algebraU is constructed; the following theorem is proved with the help of this basis: For any nonzero element Μ ∃U, there exists a finite-dimensional representation π such thatπ(u) ≠ 0.

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References

  1. 1.

    Yu. A. Drozd, S. A. Ovsienko, and V. M. Futorny, “On Gel'fand-Zetlin modules,”Suppl. Rend. Circolo Mat. Palermo, Ser. 2,26, 143–147 (1991).

  2. 2.

    V. G. Drinfel'd, “Quantum groups,” in:Proceedings of the International Mathematical Congress, Vol.1, Academic Press, Berkeley, California (1986), pp. 798–820.

  3. 3.

    M. Jimbo, “Aq-analogue ofU(gl (N+1)), Hecke Algebras, and the Yang-Baxter Equation,”Lett. Math. Phys.,11, 247–252 (1986).

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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45 No. 3, pp. 436–439, March, 1993.

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Guzner, B.Z. The Harish-Chandra theorem for the quantum algebrau q (sl (3)). Ukr Math J 45, 466–470 (1993). https://doi.org/10.1007/BF01061020

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Keywords

  • Nonzero Element