On the Irreducibility of the Complex Specialization of the Representation of The Hecke Algebra of the Complex Reflection Group G₇

2016/09/11 by Mohammad Y. Chreif, Chreif, Mohammad Y., Mohammad N. Abdulrahim +1
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Group Theory (math.GR) #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.1609.03192

openalex publication_date 2016/09/11 · openalex created_date 2016/09/23 · openalex updated_date 2026/07/28

Abstract

We consider a 2-dimensional representation of the Hecke algebra H(G₇, u), where G₇ is the complex reflection group and u is the set of indeterminates u=(x₁, x₂, y₁, y₂, y₃, z₁, z₂, z₃). After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of the representation of the Hecke algebra H(G₇, u).

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• Complex Reflection Groups and Fake Degrees
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