Transformation Groups

, Volume 3, Issue 4, pp 321–336 | Cite as

Kazhdan-Lusztig polynomials and canonical basis

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

Abstract

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 groupU q \(\mathfrak{s}\mathfrak{l}\) k . We also use known results about canonical bases forU q \(\mathfrak{s}\mathfrak{l}\)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.

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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

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