Hecke algebras and -adic groups
X He - arXiv preprint arXiv:1511.01386, 2015 - arxiv.org
This survey article, is written as an extended note and supplement of my lectures in the
current developments in mathematics conference in 2015. We discuss some recent …
current developments in mathematics conference in 2015. We discuss some recent …
The asymptotic Hecke algebra and rigidity
S Dawydiak - arXiv preprint arXiv:2312.11092, 2023 - arxiv.org
We reprove the surjectivity statement of Braverman-Kazhdan's spectral description of
Lusztig's asymptotic Hecke algebra $ J $ in the context of $ p $-adic groups. The proof is …
Lusztig's asymptotic Hecke algebra $ J $ in the context of $ p $-adic groups. The proof is …
Some results on affine Deligne–Lusztig varieties
X He - Proceedings of the International Congress of …, 2018 - World Scientific
The study of affine Deligne-Lusztig varieties originally arose from arithmetic geometry, but
many problems on affine Deligne-Lusztig varieties are purely Lie-theoretic in nature. This …
many problems on affine Deligne-Lusztig varieties are purely Lie-theoretic in nature. This …
A geometric realization of the asymptotic affine Hecke algebra
R Bezrukavnikov, I Karpov, V Krylov - arXiv preprint arXiv:2312.10582, 2023 - arxiv.org
A key tool for the study of an affine Hecke algebra $\mathcal {H} $ is provided by Springer
theory of the Langlands dual group via the realization of $\mathcal {H} $ as equivariant $ K …
theory of the Langlands dual group via the realization of $\mathcal {H} $ as equivariant $ K …
Extremal cases of Rapoport–Zink spaces
U Görtz, X He, M Rapoport - Journal of the Institute of Mathematics of …, 2022 - cambridge.org
We investigate qualitative properties of the underlying scheme of Rapoport–Zink formal
moduli spaces of p-divisible groups (resp., shtukas). We single out those cases where the …
moduli spaces of p-divisible groups (resp., shtukas). We single out those cases where the …
On the structure of the affine asymptotic Hecke algebras
R Bezrukavnikov, S Dawydiak, G Dobrovolska - Transformation Groups, 2023 - Springer
According to a conjecture of Lusztig, the asymptotic affine Hecke algebra should admit a
description in terms of the Grothedieck group of sheaves on the square of a finite set …
description in terms of the Grothedieck group of sheaves on the square of a finite set …
Shalika germs for tamely ramified elements in
O Kivinen, CC Tsai - arXiv preprint arXiv:2209.02509, 2022 - arxiv.org
Degenerating the action of the elliptic Hall algebra on the Fock space, we give a
combinatorial formula for the Shalika germs of tamely ramified regular semisimple elements …
combinatorial formula for the Shalika germs of tamely ramified regular semisimple elements …
-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras
X He, S Nie - Selecta Mathematica, 2015 - Springer
The cocenter of an affine Hecke algebra plays an important role in the study of
representations of the affine Hecke algebra and the geometry of affine Deligne–Lusztig …
representations of the affine Hecke algebra and the geometry of affine Deligne–Lusztig …
A nonabelian Fourier transform for tempered unipotent representations
AM Aubert, D Ciubotaru, B Romano - arXiv preprint arXiv:2106.13969, 2021 - arxiv.org
We define an involution on the space of compact tempered unipotent representations of
inner twists of a split simple $ p $-adic group $ G $ and investigate its behaviour with respect …
inner twists of a split simple $ p $-adic group $ G $ and investigate its behaviour with respect …
Denominators in Lusztig's asymptotic Hecke algebra via the Plancherel formula
S Dawydiak - arXiv preprint arXiv:2110.07148, 2021 - arxiv.org
Let $\tilde {W} $ be an extended affine Weyl group, $\mathbf {H} $ be the corresponding
affine Hecke algebra over the ring $\mathbb {C}[\mathbf {q}^\frac {1}{2},\mathbf {q}^{-\frac …
affine Hecke algebra over the ring $\mathbb {C}[\mathbf {q}^\frac {1}{2},\mathbf {q}^{-\frac …