Invariants for representations of Weyl groups and two-sided cells
The notion of two-sided cell, which was originally introduced by A.~Joseph and reformulated by D.~Kazhdan and G.~Lusztig, has played an important role in representation theory. Results concerning them have been obtained by very deep and sometimes ad hoc arguments. Here we introduce certain polynomial invariants for irreducible representations of Weyl groups. Our invariants are easily calculated, and the calculational results show that they almost determine the two-sided cells. Moreover, the factorization pattern of our polynomial invariants seems to be controlled by the natural parameter set \({\mathcal M}({\mathcal G})\) of each two-sided cell. Recently N.~Kawanaka introduced a new invariant, whose definition resembles the invariants studied in the present paper. We studied Kawanaka's invariants, and observed again a similar relation as above. This observation is discussed elsewhere.
irreducible representations of Weyl groups
scientific article; zbMATH DE number 1336905