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Eigenvalue of Iwahori Hecke Algebra element for the Steinberg

In Iwahori-Matsumoto's paper the Iwahori Hecke Algebra for $G=GL_n(F)$ is generated by $X_{s_0}, X_{s_i},i\in\{0,...,n-1\}$ and $ X_{\rho}$ with the relations: $ 1) (X_{s_{i}}-q)(X_{s_{i}}+1)=0\:,\;\ …
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