{
"id": "1901.02323",
"version": "v1",
"published": "2019-01-08T14:35:08.000Z",
"updated": "2019-01-08T14:35:08.000Z",
"title": "The ABC of p-Cells",
"authors": [
"Lars Thorge Jensen"
],
"comment": "36 pages, best viewed in colour",
"categories": [
"math.RT",
"math.CO",
"math.GR"
],
"abstract": "Parallel to the very rich theory of Kazhdan-Lusztig cells in characteristic $0$, we try to build a similar theory in positive characteristic. We study cells with respect to the $p$-canonical basis of the Hecke algebra of a crystallographic Coxeter system (see arXiv:1510.01556(2)). Our main technical tool are the star-operations introduced by Kazhdan-Lusztig which have interesting numerical consequences for the $p$-canonical basis. As an application, we explicitely describe $p$-cells in finite type $A$ (i.e. for symmetric groups) using the Robinson-Schensted correspondence. Moreover, we show that Kazhdan-Lusztig cells in finite types $B$ and $C$ decompose into $p$-cells for $p > 2$.",
"revisions": [
{
"version": "v1",
"updated": "2019-01-08T14:35:08.000Z"
}
],
"analyses": {
"subjects": [
"20C08",
"20B05",
"05E10"
],
"keywords": [
"kazhdan-lusztig cells",
"finite type",
"crystallographic coxeter system",
"canonical basis",
"characteristic"
],
"note": {
"typesetting": "TeX",
"pages": 36,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}