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 the 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 MðGÞ of each two-sided cell.wðwÞt l 0 ðwÞ ð0:2Þafter such modification, where w ¼ trace r.Concerning the function (0.2), we can make the following observation by a case study. Let w, w 0 A W 4 , where W 4 is the set of irreducible characters of W. Then the
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.