An Elementary Proof of Roichman’s Rule for Irreducible Characters of Iwahori-Hecke Algebras of Type A
The purpose of this note is to give an elementary proof of a recent formula of Y. Roichman [Ro] which describes the irreducible characters of the Iwahori-Hecke algebras of type A. Roichman’s original proof is via a detailed analysis of the action of certain elements in the Iwahori-Hecke algebra in the terms of the Kazhdan-Lusztig basis of each irreducible representation. Here we shall show that the Robinson-Schensted-Knuth insertion algorithm can be used to show that Roichman’s rule is equivalent to the “Frobenius formula” for the characters of the Iwahori-Hecke algebras [Ra].
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