Skip to main content
SpringerLink
Log in

Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We shall give a generalization of the Littlewood-Richardson rule forU q (g) associated with, the classical Lie algebras by use of crystal base. This rule describes explicitly the decomposition of tensor products of given representations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [B-Z] Berenstein, A.D., Zelevinski, A.V.: Tensor product multiplicities and convex polytopes in partition, space. J. Geom. Phys.5, 453–472 (1989)

    Google Scholar 

  • [D] Drinfeld, V.G.: Quantum Groups. ICM proceedings, Berkely, 798–820 (1986)

  • [J] Jimbo, M.: Aq-difference analogue ofU(g) and the Yang-Baxter equation. Lett. Math. Phys.11, 247–252 (1986)

    Google Scholar 

  • [K1] Kashiwara, M.: Crystallizing theq-analogue of universal enveloping algebra. Commun. Math. Phys.133, 249–260 (1990)

    Google Scholar 

  • [K2] Kashiwara, M.: On crystal base ofq-analogue of universal enveloping algebras. Duke. Math. J.63, 465–516 (1991)

    Google Scholar 

  • [K-N] Kashiwara, M., Nakashima, T.: Crystal graphs for Representations of theq-analogue of Classical Lie Algebras. RIMS preprint,767 (1991)

  • [L] Littelmann, P.: A Generalization of the Littlewood-Richardson Rule. J. Algebra130, 328–368 (1990)

    Google Scholar 

  • [M] Macdonald, I.G.: Symmetric Functions and Hall Polynomials. Oxford: Clarendon Press 1979

    Google Scholar 

  • [N] Nakashima, T.: A basis of symmetric tensor representations for the quantum analogue of the Lie algebraB n ,C n , andD n . Publ. RIMS. Kyoto. Univ.26, 723–733 (1990)

    Google Scholar 

  • [O] Okado, M.: QuantumR Matrices Related to the spin Representations ofB n andD n . Commun. Math. Phys.134, 467–486 (1990)

    Google Scholar 

  • [Re] Reshetikhin, N.Yu.: Quantized universal enveloping algebras. Yang-Baxter equation, and invariants of links I. LOMI preprint E-4-48 (1990)

  • [T] Thomas, G.: On Schensted's construction and the multiplication of Schur function. Adv. Math.30, 8–32 (1978)

    Google Scholar 

  • [W] Weyman, J.: Pieri's formulas for classical groups. Contemp. Math.88, 177–184 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Science, Faculty of Engineering Science, Osaka University, 560, Toyonaka Osaka, Japan

    Toshiki Nakashima

Authors
  1. Toshiki Nakashima
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by N. Yu. Reshetikhin

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nakashima, T. Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras. Commun.Math. Phys. 154, 215–243 (1993). https://doi.org/10.1007/BF02096996

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02096996

Keywords

Search

Navigation