Abstract
In this paper, we determine $\tilde{\tau}_q\bigl(\chi^\lambda_q\bigr)$, the Gauss sums on the Iwahori-Hecke algebras of type $A$ for irreducible characters $\chi^\lambda_q$, which are $q$-analogues of those on the symmetric groups. We also explicitly determine the values of the corresponding trace function $\psi^{(n)}_q=\sum_{\lambda \vdash n} \tilde{\tau}_q\bigl(\chi^\lambda_q\bigr) \chi^\lambda_q$.
Citation
Yasushi GOMI. "Gauss Sums on the Iwahori-Hecke Algebras of Type $A$." Tokyo J. Math. 39 (3) 583 - 596, March 2017. https://doi.org/10.3836/tjm/1491465731