We review the construction of generalized affine Hecke algebras attached to Bernstein series of both smooth irreducible and enhanced $L$-parameters of $p$-adic reductive groups and apply it to the study of the Howe correspondence.
On special representations of $p$-adic reductive groups
On Hecke algebras for $p$-adic reductive groups: The example of $G_2$
Local Summability of Characters on $p$-adic Reductive Groups
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