Centers and cocenters of 0-Hecke algebras

He, Xuhua

doi:10.1007/978-3-319-23443-4_8

Cited by 6 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For finite Hecke algebras, it is proved in [He15, Theorem 5.5], where the basis theorem ofH q (for nonzero parameters q) is used. A different and simpler approach is found in [HNx,§2.4], which works for both finite and affine Hecke algebras. For any Σ ∈W min / ≈ corresponding to a standard quadruple (J, x, K, C), we set J Σ = J.…”

Section: Rigid Determinantmentioning

confidence: 99%

See 1 more Smart Citation

Hecke algebras and $p$-adic groups

2015

Current Developments in Mathematics

Self Cite

View full text Add to dashboard Cite

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 developments on the conjugacy classes of affine Weyl groups and p-adic groups, and some applications to Shimura varieties and to representations of affine Hecke algebras. 74 X. HE 2.12. Application 117 3. Part III. Cocenters of affine Hecke algebras 119 3.1. Motivation: group algebras 119 3.2. Hecke algebras 119 3.3. Finite Hecke algebras 121 3.4. Representations of affine Hecke algebras and of p-adic groups 3.5. Affine Hecke algebras 122 3.6. Cocenter-representation duality for affine Hecke algebras 3.7. The "Modular case" 126 3.8. 0-Hecke algebras 130 References 132

show abstract

Section: Rigid Determinantmentioning

confidence: 99%

“…Here the equivalence between (1) and (2) is first obtained by Vignéras in [Vig14]. The criterion (3) for the supersingular modules is given in [HNx,Proposition 5.4] and a new proof of the equivalence between (1) and (2) is also given in loc.cit.…”

mentioning

confidence: 97%

Hecke algebras and $p$-adic groups

2015

Current Developments in Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [7], Lusztig gave a basis of the center of affine Hecke algebras. In [6], He also mentioned a similar proof could be applied to give a basis of the center of affine 0-Hecke algebras. The basis is closely related to finite conjugacy classes in W aff .…”

Section: Introductionmentioning

confidence: 96%

“…0-Hecke algebras are deformations of the group algebras of finite Coxeter groups with zero parameter. In [6], He gave a basis of the center of 0-Hecke algebras associated to finte Coxeter groups. The basis is closely related to maximal length elements in the conjugacy classes of W .…”

Section: Introductionmentioning

confidence: 99%

Center of $\mathcal{H}_R(0,c_{\tilde{s}})$ associated to a pro-$p$-Iwahori Weyl group

Gao

2018

Preprint

View full text Add to dashboard Cite

Let W be an Iwahori Weyl group and W (1) be an extension of W by an abelian group. In [11], Vigneras gave a description of the R-algebra HR(qs, cs) associated to W (1), and in [12], Vigneras gave a basis of the center of HR(qs, cs) using the Bernstein presentation of HR(qs, cs). In this paper, we restrict to the case where qs = 0 and use the Iwahori-Matsumoto presentation to give a basis of the center of HR(0, cs).

show abstract

“…These results on conjugacy classes were later reused in other domains involving Weyl group elements (e.g. Bruhat cells [EG04, CLT10, Lus11a], Deligne-Lusztig varieties [BR08, OR08], 0-Hecke algebras [He15] and partitions of the wonderful compactification [He07]), and in particular He-Lusztig applied them to construct cross sections in reductive groups out of elliptic Weyl group elements of minimal length [HL12].…”

Section: Introductionmentioning

confidence: 99%

Minimally dominant elements of finite Coxeter groups

Malten

2021

Preprint

View full text Add to dashboard Cite

Recently, Lusztig constructed for each reductive group a partition by unions of sheets of conjugacy classes, which is indexed by a subset of the set of conjugacy classes in the associated Weyl group. Sevostyanov subsequently used certain elements in each of these Weyl group conjugacy classes to construct strictly transverse slices to the conjugacy classes in these strata, generalising the classical Steinberg slice, and similar cross sections were built out of different Weyl group elements by He-Lusztig.In this paper we observe that He-Lusztig's and Sevostyanov's Weyl group elements share a certain geometric property, which we call minimally dominant; for example, we show that this property characterises involutions of maximal length. Generalising He-Nie's work on twisted conjugacy classes in finite Coxeter groups, we explain for various geometrically defined subsets that their elements are conjugate by simple shifts, cyclic shifts and strong conjugations. We furthermore derive for a large class of elements that the principal Deligne-Garside factors of their powers in the braid monoid are maximal in some sense. This includes those that are used in He-Lusztig's and Sevostyanov's cross sections, and explains their appearance there; in particular, all minimally dominant elements in the aforementioned conjugacy classes yield strictly transverse slices. These elements are conjugate by cyclic shifts, their Artin-Tits braids are never pseudo-Anosov in the conjectural Nielsen-Thurston classification and their Bruhat cells should furnish an alternative construction of Lusztig's inverse to the Kazhdan-Lusztig map and of his partition of reductive groups.

show abstract

Centers and cocenters of 0-Hecke algebras

Abstract: Abstract. In this paper, we give explicit descriptions of the centers and cocenters of 0-Hecke algebras associated to finite Coxeter groups.

Cited by 6 publications

References 12 publications

Hecke algebras and $p$-adic groups

Hecke algebras and $p$-adic groups

Center of $\mathcal{H}_R(0,c_{\tilde{s}})$ associated to a pro-$p$-Iwahori Weyl group

Minimally dominant elements of finite Coxeter groups

Contact Info

Product

Resources

About