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Kazhdan-Lusztig polynomials and canonical basis

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arxiv q-alg/9709042 v1 pith:FKSKMJWE submitted 1997-09-29 q-alg math.QA

Igor Frenkel , Mikhail Khovanov , Alexander Kirillov Jr This is my paper · ORCID
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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 $n$th tensor power of the fundamental representation of the quantum group $U_q sl_k$. We also use known results about canonical bases for $U_q sl_2$ to get a new proof of recurrent formulas for KL polynomials for maximal parabolic subgroups (geometrically, this case corresponds to Grassmanians), due to Lascoux-Schutzenberger and Zelevinsky.

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  1. Big data approach to Kazhdan-Lusztig polynomials

    math.RT 2024-12 conditional novelty 6.0 of 10

    Data on Kazhdan-Lusztig polynomials up to S_11 suggests superexponential growth of extremal coefficients, near-universal unimodality, and a conjectured closed family (1+v+...+v^l)^{k-1}.

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