2024/12/27 by Ben Elias, Elias, Ben
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2412.19749
openalex publication_date 2024/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this short, elementary note we prove that if a faithful reflection representation of a Coxeter group preserves an orthant, then that Coxeter group is a product of symmetric groups acting on its natural permutation representation. We also prove an affine analogue of this statement, where an orthant is preserved modulo an invariant sublattice. As a consequence, the existence of two different versions of the quantum geometric Satake equivalence is a purely type A phenomenon.