Hecke Algebra-valued Poincaré Series and Geometric Factorization of Affine Weyl Groups

[1903.00703] Hecke Algebra-valued Poincaré Series and Geometric Factorization of Affine Weyl Groups Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Group Theory arXiv:1903.00703 (math) [Submitted on 2 Mar 2019 ( v1 ), last revised 17 Aug 2026 (this version, v3)] Title: Hecke Algebra-valued Poincaré Series and Geometric Factorization of Affine Weyl Groups Authors: Ming-Hsuan Kang , Jiu Kang Yu View a PDF of the paper titled Hecke Algebra-valued Poincar\'e Series and Geometric Factorization of Affine Weyl Groups, by Ming-Hsuan Kang and 1 other authors View PDF HTML (experimental) Abstract: This paper studies affine Weyl groups through the geometry of geodesic tubes and their hyperbolic stabilizers. We introduce a geometric framework relating affine Weyl group factorizations to Hecke-algebra-valued Poincaré series and zeta functions on quotient complexes. Using this framework, we prove a conjecture describing the connection between geodesic tubes and factorizations of Poincaré series for affine Weyl groups. We also establish partial results toward a Hecke-algebra-valued zeta identity for simply connected groups, including the cases of types $\widetilde{A}_{n-1}$ and $\widetilde{C}_n$. These results highlight the interaction between affine Weyl group geometry, Hecke algebras, and zeta functions arising from Bruhat--Tits buildings. Subjects: Group Theory (math.GR) Cite as: arXiv:1903.00703 [math.GR] (or arXiv:1903.00703v3 [math.GR] for this version) https://doi.org/10.48550/arXiv.1903.00703 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ming-Hsuan Kang [ view email ] [v1] Sat, 2 Mar 2019 13:38:46 UTC (20 KB) [v2] Mon, 6 Nov 2023 07:15:04 UTC (40 KB) [v3] Mon, 17 Aug 2026 03:05:05 UTC (40 KB) Full-text links: Access Paper: View a PDF of the paper titled Hecke Algebra-valued Poincar\'e Series and Geometric Factorization of Affine Weyl Groups, by Ming-Hsuan Kang and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.GR < prev | next > new | recent | 2019-03 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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