Kazhdan-lusztig polynomials and canonical basis

I. B. Frenkel; M. G. Khovanov; A. A. Kirillov

doi:10.1007/BF01234531

Kazhdan-lusztig polynomials and canonical basis

I. B. Frenkel
, M. G. Khovanov
, A. A. Kirillov

Mathematics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

In this paper we show that the Kazhdan-Lusztig polynomials (and, more generally, parabolic KL polynomials) for the group S_n coincide with the coefficients of the canonical basis in nth tensor power of the fundamental representation of the quantum group U_qsl_k. We also use known results about canonical bases for U_qsl₂ 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.

Original language	English
Pages (from-to)	321-336
Number of pages	16
Journal	Transformation Groups
Volume	3
Issue number	4
DOIs	https://doi.org/10.1007/BF01234531
State	Published - 1998

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abstract = "In this paper we show that the Kazhdan-Lusztig polynomials (and, more generally, parabolic KL polynomials) for the group Sn coincide with the coefficients of the canonical basis in nth tensor power of the fundamental representation of the quantum group Uqslk. We also use known results about canonical bases for Uqsl2 to get a new proof of recurrent formulas for KL polynomials for maximal parabolic subgroups (geometrically, this case corresponds to Grassmannians), due to Lascoux-Sch{\"u}tzenberger and Zelevinsky.",

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journal = "Transformation Groups",

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AU - Frenkel, I. B.

AU - Khovanov, M. G.

AU - Kirillov, A. A.

PY - 1998

Y1 - 1998

N2 - In this paper we show that the Kazhdan-Lusztig polynomials (and, more generally, parabolic KL polynomials) for the group Sn coincide with the coefficients of the canonical basis in nth tensor power of the fundamental representation of the quantum group Uqslk. We also use known results about canonical bases for Uqsl2 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.

AB - In this paper we show that the Kazhdan-Lusztig polynomials (and, more generally, parabolic KL polynomials) for the group Sn coincide with the coefficients of the canonical basis in nth tensor power of the fundamental representation of the quantum group Uqslk. We also use known results about canonical bases for Uqsl2 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.

UR - https://www.scopus.com/pages/publications/0032282754

U2 - 10.1007/BF01234531

DO - 10.1007/BF01234531

M3 - Article

SN - 1083-4362

VL - 3

SP - 321

EP - 336

JO - Transformation Groups

JF - Transformation Groups

IS - 4

ER -

Kazhdan-lusztig polynomials and canonical basis

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