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Kazhdan-Lusztig polynomials and canonical basis

Igor Frenkel·Mikhail Khovanov·Alexander Kirillov Jr
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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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BibTeXRIS

Igor Frenkel, Mikhail Khovanov, Alexander Kirillov Jr. 1997-09-29. Kazhdan-Lusztig polynomials and canonical basis. https://arxiv.org/abs/q-alg/9709042

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