This paper studies the wall and chamber structure of algebras via generic decompositions of g-vectors. Specifically, we examine points outside the chambers of the wall and chamber structure of ($\tau$-tilting infinite) finite-dimensional algebras. We demonstrate that the cones of g-vectors are both rational and simplicial. Moreover, we show that the open cone of a given g-vector and the interior of its TF-equivalence class coincide if and only if they are of the same dimension. Furthermore, we establish that g-vectors satisfy the ray condition when sufficiently far from the origin. These results allow us to generalize several findings by Asai and Iyama regarding TF-equivalence classes of g-vectors.
Categories: math.RT