Summary: We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl groups with respect to the Kazhdan-Lusztig basis, this agrees with Lusztig's notion of a special module introduced in [Lu1].

16G10, 16W99, 20C08

algebra, positive basis, idempotent, cell, cell representation, special representation