Special Modules over Positively Based Algebras

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].

2010 Mathematics Subject Classification: 16G10; 16W99; 20C08

Keywords and Phrases: algebra; positive basis; idempotent; cell; cell representation; special representation

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