Tokyo Journal of Mathematics

Gauss Sums on the Iwahori-Hecke Algebras of Type $A$

Yasushi GOMI

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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 $\psi^{(n)}_q=\sum_{\lambda \vdash n} \tilde{\tau}_q\bigl(\chi^\lambda_q\bigr) \chi^\lambda_q$.

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Tokyo J. Math., Volume 39, Number 3 (2017), 583-596.

First available in Project Euclid: 6 April 2017

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GOMI, Yasushi. Gauss Sums on the Iwahori-Hecke Algebras of Type $A$. Tokyo J. Math. 39 (2017), no. 3, 583--596. doi:10.3836/tjm/1491465731.

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