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Property š‘…<sub>āˆž</sub> for some spherical and affine Artinā€“Tits groups

Property š‘…<sub>āˆž</sub> for some spherical and affine Artinā€“Tits groups

Abstract Let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>ā©¾</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> n\geqslant 2 . In this note, we give a short uniform proof of property <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>R</m:mi> <m:mi mathvariant="normal">āˆž</m:mi> </m:msub> </m:math> R_{\infty} for the Artinā€“Tits groups of spherical types <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>A</m:mi> <m:mi>n</m:mi> </m:msub> </m:math> A_{n} , <m:math ā€¦