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arXiv:1901.02323 [math.RT]AbstractReferencesReviewsResources

The ABC of p-Cells

Lars Thorge Jensen

Published 2019-01-08Version 1

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 $p > 2$.

Comments: 36 pages, best viewed in colour
Categories: math.RT, math.CO, math.GR
Subjects: 20C08, 20B05, 05E10
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