Transformation Groups

, Volume 3, Issue 4, pp 321–336

Kazhdan-Lusztig polynomials and canonical basis

  • I. B. Frenkel
  • M. G. Khovanov
  • A. A. KirillovJr.

DOI: 10.1007/BF01234531

Cite this article as:
Frenkel, I.B., Khovanov, M.G. & Kirillov, A.A. Transformation Groups (1998) 3: 321. doi:10.1007/BF01234531


In this paper we show that the Kazhdan-Lusztig polynomials (and, more generally, parabolic KL polynomials) for the groupSn coincide with the coefficients of the canonical basis innth tensor power of the fundamental representation of the quantum groupUq\(\mathfrak{s}\mathfrak{l}\)k. We also use known results about canonical bases forUq\(\mathfrak{s}\mathfrak{l}\)2 to get a new proof of recurrent formulas for KL polynomials for maximal parabolic subgroups (geometrically, this case corresponds to Grassmannians), due to Lascoux-Schützenberger and Zelevinsky.

Copyright information

© Birkhäuser 1998

Authors and Affiliations

  • I. B. Frenkel
    • 1
  • M. G. Khovanov
    • 2
  • A. A. KirillovJr.
    • 3
  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  3. 3.Department of MathematicsMITCambridgeUSA