1 | | One quick question outside of finite type Weyl and Coxeter groups {{{W}}}: is it correct that the actions of {{{W}}} on {{{V}}} and on {{{V^*}}} are the same. This is, the image of (x1,...,xn) under {{{w}}} is the same for (x1,...,xn) being a vector in {{{V}}} expressed in the basis {ei} and being a vector in {{{V^*}}} ~~being ~~expressed in the dual basis {xi}? |

| 1 | One quick question outside of finite type Weyl and Coxeter groups {{{W}}}: is it correct that the actions of {{{W}}} on {{{V}}} and on {{{V^*}}} are the same. This is, the image of (x1,...,xn) under {{{w}}} is the same for (x1,...,xn) being a vector in {{{V}}} expressed in the basis {ei} and being a vector in {{{V^*}}} expressed in the dual basis {xi}? |