6 papers · 1 filter
On Braverman-Kazhdan's asymptotic Hecke algebra for inner forms of
Stefan Dawydiak
We study Braverman-Kazhdan's asymptotic Hecke algebra for inner forms of -adic . We show that and the property for a -rep…
Standard modules of affine Hecke algebras
Stefan Dawydiak
Let be a connected reductive group defined and split over a non-archimedean local field . We give a new geometric proof of a special case of a recent theorem of Solleveld. N…
A positivity property in the based ring of the lowest two-sided cell
Stefan Dawydiak
Let be an extended affine Weyl group and and be the corresponding affine and asymptotic Hecke algebras with standard bases and $\{t_w\…
The asymptotic Hecke algebra and rigidity
Stefan Dawydiak
We reprove the surjectivity statement of Braverman-Kazhdan's spectral description of Lusztig's asymptotic Hecke algebra in the context of -adic groups. The proof is based on…
Denominators in Lusztig's asymptotic Hecke algebra via the Plancherel formula
Stefan Dawydiak
Let be an extended affine Weyl group, be the corresponding affine Hecke algebra over the ring $\mathbb{C}[\mathbf{q}^\frac{1}{2}, \mathbf{q}^{-\frac{1}{2}}…
A coherent categorification of the based ring of the lowest two-sided cell
Stefan Dawydiak
We give a partial coherent categorification of , the based ring of the lowest two sided cell of an affine Weyl group, equipped with a monoidal functor from the category of coh…