Hazi, A. ORCID: 0000000172642211 (2020). Matrix recursion for positive characteristic diagrammatic Soergel bimodules for affine Weyl groups. .
Abstract
Let $W$ be an affine Weyl group, and let $\Bbbk$ be a field of characteristic $p>0$. The diagrammatic Hecke category $\mathcal{D}$ for $W$ over $\Bbbk$ is a categorification of the Hecke algebra for $W$ with rich connections to modular representation theory. We explicitly construct a functor from $\mathcal{D}$ to a matrix category which categorifies a recursive representation $\xi : \mathbb{Z}W \rightarrow M_{p^r}(\mathbb{Z}W)$, where $r$ is the rank of the underlying finite root system. This functor gives a method for understanding diagrammatic Soergel bimodules in terms of other diagrammatic Soergel bimodules which are "smaller" by a factor of $p$. It also explains the presence of selfsimilarity in the $p$canonical basis, which has been observed in small examples. By decategorifying we obtain a new lower bound on the $p$canonical basis, which corresponds to new lower bounds on the characters of the indecomposable tilting modules by the recent $p$canonical tilting character formula due to AcharMakisumiRicheWilliamson.
Publication Type:  Monograph (Working Paper) 

Additional Information:  62 pages, many figures, best viewed in color 
Subjects:  Q Science > QA Mathematics 
Departments:  School of Mathematics, Computer Science & Engineering > Mathematics 
Related URLs:  
Date Deposited:  27 May 2020 08:59 
URI:  https://openaccess.city.ac.uk/id/eprint/23593 

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