dorsal/arxiv
View SchemaKazhdan-Lusztig polynomials and canonical basis
| Authors | Igor Frenkel, Mikhail Khovanov, Alexander Kirillov Jr |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9709042 |
| URL | https://arxiv.org/abs/q-alg/9709042 |
| Journal | Transform. Groups 3 (1998), no. 4, 321--336 |
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.
{
"annotation_id": "94519451-d157-43da-8980-7bdf35ed5f8b",
"date_created": "2026-03-02T18:01:28.418000Z",
"date_modified": "2026-03-02T18:01:28.418000Z",
"file_hash": "2d5d5f525720edb599a1cf4332cf96ea8a4006ca7de57149011e62186e85fefa",
"private": false,
"record": {
"abstract": "In this paper we show that the Kazhdan-Lusztig polynomials (and, more\ngenerally, parabolic KL polynomials) for the group $S_n$ coincide with the\ncoefficients of the canonical basis in $n$th tensor power of the fundamental\nrepresentation of the quantum group $U_q sl_k$. We also use known results about\ncanonical bases for $U_q sl_2$ to get a new proof of recurrent formulas for KL\npolynomials for maximal parabolic subgroups (geometrically, this case\ncorresponds to Grassmanians), due to Lascoux-Schutzenberger and Zelevinsky.",
"arxiv_id": "q-alg/9709042",
"authors": [
"Igor Frenkel",
"Mikhail Khovanov",
"Alexander Kirillov Jr"
],
"categories": [
"q-alg",
"math.QA"
],
"journal_ref": "Transform. Groups 3 (1998), no. 4, 321--336",
"title": "Kazhdan-Lusztig polynomials and canonical basis",
"url": "https://arxiv.org/abs/q-alg/9709042"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "93d48ef8-cd95-45ac-8fe2-9cd386a1eb9f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}