Robinson-Schensted-Knuth Insertion And Characters Of Cyclotomic Hecke Algebras

this paper we derive the formula q = X ##Pn,r X Q# wt q,u (Q# ) s # , where Q# ranges over the set of "standard tableaux" of shape #, and where wt q,u is a weight on standard tableaux that depends on the parameters q and u i and that is computed combinatorially. By comparing coe#cients of s # in these two formulas we obtain the expression # # q (a )= X Q# wt q,u (Q# ) which computes the irreducible H n,r -characters as a sum over standard tableaux. When q = 1 and u i = # i our character formula specializes to a character formula for the complex reflection group G n,r . In the special case where n = r = 1, the cyclotomic Hecke algebra H 1,1 is the Iwahori-Hecke algebra H n (q)oftypeA n-1 associated with the symmetric group S n . Shoji's Frobenius formula specializes, in this case, to the Frobenius formula of A. Ram [Ra1] for H n (q) and our character formula is a generalization of the Roichman formula [Ro] for irreducible characters of H n (q) and S