2019/03/02 by Ming-Hsuan Kang, Kang, Ming-Hsuan, Jiu Kang Yu +1
Chemistry · Mathematics · #Advanced Algebra and Geometry #Axial and Atropisomeric Chirality Synthesis #FOS: Mathematics #Group Theory (math.GR) #Molecular spectroscopy and chirality
paper · pdf · doi:10.48550/arxiv.1903.00703
openalex publication_date 2019/03/02 · openalex created_date 2023/11/09 · openalex updated_date 2026/07/28
This paper explores affine Weyl groups and their associated Hecke algebras, concentrating on the Poincaré series with coefficients in Hecke algebra. We investigate its relationship with zeta functions on complexes and extend existing research on geodesic tubes to encompass higher dimensions. Our main findings confirm a conjecture that elucidates the connection between the Poincaré series and geodesic tubes. Additionally, we provide partial evidence for another conjecture related to the zeta identity for simply connected groups. These contributions deepen our understanding of the interactions among algebraic groups, Hecke algebras, and the geometry of related complexes.