Center of pro-p-Iwahori-Hecke algebra
| dc.contributor.advisor | He, Xuhua | en_US |
| dc.contributor.author | Gao, Yijie | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2019-09-26T05:33:40Z | |
| dc.date.available | 2019-09-26T05:33:40Z | |
| dc.date.issued | 2019 | en_US |
| dc.description.abstract | Let G be a connected reductive group over a p-adic eld F. The study of representations of G(F) naturally involves the pro-p-Iwahori-Heche algebra of G(F). The pro-p-Iwahori-Hecke algebra is a deformation of the group algebra of the pro-p-Iwahori Weyl group of G(F) with generic parameters. The pro- p-Iwahori-Hecke algebra with zero parameters plays an important role in the study of mod-p representations of G(F). In a series of paper, Vigneras introduced a generic algebra HR(q~s; c~s) which generalizes the pro-p-Iwahori-Hecke algebra of a reductive p-adic group. Vign- eras also gave a basis of the center of HR(q~s; c~s) when HR(q~s; c~s) is associated with a pro-p-Iwahori Weyl group. This basis is dened by using the Bernstein presentation of HR(q~s; c~s) and the alcove walk. In this article, we restrict to the case where q~s = 0 and give an explicit description of the center of HR(0; c~s) using the Iwahori-Matsumoto presentation. First, we introduce the generic algebra. Let W be the semidirect product of a Coxeter group and a group acting on the Coxeter group and stabilizing the generating set of the Coxeter group. Let W(1) be an extension of W with a commutative group. Let R be a commutative ring. We give the denition of the R-algebra HR(q~s; c~s) of W(1) with parameters (q~s; c~s). Then for any pair (v;w) in W W with v w, we dene a linear operator rv;w between R-submodules of HR(q~s; c~s). It takes some work to show that rv;w is well dened. Next, we restrict W to be an IwahoriWeyl group. We show that the maximal length terms of a central element in HR(q~s; c~s) is given by a union of nite conjugacy classes in W(1). Then we prove some techical results regarding rv;w acting on the maximal length terms of a central element in HR(q~s; c~s). In the last part, we restrict to the case when q~s = 0 and give a explicit basis of the center of HR(0; c~s) in the Iwahori-Matsumoto presentation by using the operator rv;w. Two examples are given to help understand how this basis looks like. | en_US |
| dc.identifier | https://doi.org/10.13016/2y5h-nsl2 | |
| dc.identifier.uri | http://hdl.handle.net/1903/24945 | |
| dc.language.iso | en | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.title | Center of pro-p-Iwahori-Hecke algebra | en_US |
| dc.type | Dissertation | en_US |
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