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We describe an algorithm for computing the $p$-canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category directly, but rather uses a faithful embedding of the Hecke category inside
Externí odkaz:
http://arxiv.org/abs/2204.04924
In the Iwahori-Hecke algebra, the full twist acts on cell modules by a scalar, and the half twist acts by a scalar and an involution. A categorification of this statement, describing the action of the half and full twist Rouquier complexes on the Hec
Externí odkaz:
http://arxiv.org/abs/2111.12190
Autor:
Jensen, Lars Thorge
A new algorithm allows us to calculate many new tilting characters for $SL_3$, $SP_4$, $G_2$, $SL_4$ and potentially many other groups. These calculations show that the Lusztig-Williamson Billiards Conjecture needs to be corrected. In this paper we p
Externí odkaz:
http://arxiv.org/abs/2105.04665
Autor:
Jensen, Lars Thorge
For symmetric groups we show that the p-canonical basis can be extended to a cell datum for the Iwahori-Hecke algebra H and that the two-sided p-cell preorder coincides with the Kazhdan-Lusztig two-sided cell preorder. Moreover, we show that left (or
Externí odkaz:
http://arxiv.org/abs/2009.11715
Autor:
Jensen, Lars Thorge, Patimo, Leonardo
We study cells with respect to the $p$-canonical basis of the Hecke algebra of a crystallographic Coxeter system (see arXiv:1510.01556, arXiv:1901.02323) and their compatibility with standard parabolic subgroups. We show that after induction to the s
Externí odkaz:
http://arxiv.org/abs/1911.08969
Autor:
Jensen, Lars Thorge
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 sy
Externí odkaz:
http://arxiv.org/abs/1901.02323
We describe a positive characteristic analogue of the Kazhdan-Lusztig basis of the Hecke algebra of a crystallographic Coxeter system and investigate some of its properties. Using Soergel calculus we describe an algorithm to calculate this basis. We
Externí odkaz:
http://arxiv.org/abs/1510.01556
Autor:
Jensen, Lars Thorge
We investigate the relation between the Garside normal form for positive braids and the $2$-braid group defined by Rouquier. Inspired by work of Brav and Thomas we show that the Garside normal form is encoded in the action of the $2$-braid group on a
Externí odkaz:
http://arxiv.org/abs/1505.05353
Akademický článek
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Publikováno v:
Transformation Groups.
We describe an algorithm for computing the $p$-canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category directly, but rather uses a faithful embedding of the Hecke category inside
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::019011e287d4283bf30d5b60fb80337a
https://doi.org/10.1007/s00031-023-09799-z
https://doi.org/10.1007/s00031-023-09799-z
