Abstract
Let F be a non-Archimedean local field and Let be an irreducible smooth Iwahori-spherical representation of G. It is easy to see that such representations are always self-dual. The space V of π admits a non-degenerate G-invariant bilinear form which is unique up to scaling. It can be shown that the form is either symmetric or skew-symmetric and we set accordingly. In this article, we use the Bernstein–Lusztig presentation of the Iwahori–Hecke algebra of G and show that
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