首页/论文/2005.02622

arXiv 2005.026222020-05math.RTmath.NT

Comparison of types for inner forms of $\mathrm{GL}_{N}$

Yuki Yamamoto

备注：: 47 pages

英文摘要：

Let $F$ be a non-archimedean local field, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. To construct types for supercuspidal representations of $G$, simple types by Sécherre--Stevens and Yu's construction are already known. In this paper, we compare these constructions. In particular, we show essentially tame supercuspidal representations of $G$ defined by Bushnell--Henniart are nothing but tame supercuspidal representations defined by Yu.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

$\mathrm{GSp}_{2n}$ 及其内形式的离散系列表示对应

Correspondence of discrete series representations of $\mathrm{GSp}_{2n}$ and its inner form

对于 $p>2$ 和 $n\geq 2$，在 $p$-adic 域上的 $\mathrm{GSp}_{2n}$ 及其内形式的离散系列表示之间构造了具有特征方程的对应，推广了 Chan 和 Gan 的工作以及局部 Jacquet-Langlands 对应，并部分揭示了 $\mathrm{GSp}_{2n}$ 及其内形式在 $p$-adic 域上的局部 Langlands 对应。

2026-06-03math.NTmath.RT

On the types for supercuspidal representations of inner forms of $\mathrm{GL}_{N}$

Let $F$ be a non-Archimedean local field, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. It is known that for every irreducible supercuspidal representation $π$, there exists a $[G, π]_{G}$-type $(J, λ)$, called a (maximal) simple type. We will show that $[G, π]_{G}$-types defined over some maximal compact subgroup are unique up to $G$-conjugations under some unramifiedness assumption on a simple stratum.

2019-11-12math.NTmath.RT

格尔福恩-基里洛夫维数与模 $p$ 余数上同调对于 $\mathrm{GL}_2$ 的内形式

Gelfand--Kirillov dimension and mod $p$ cohomology for inner forms of $\mathrm{GL}_2$

King’s College London（伦敦国王学院）；Northwestern University（西北大学）

本文计算了内形式 $D^\times$ 的模 $p$ 上同调中海德克特征空间的格尔福恩-基里洛夫维数，并在 $D$ 在 $p$ 处为除环时给出了简化证明。

2026-04-16math.NTmath.RT

$p$-adic 域上 $\mathrm{GL}_n$ 内形式的共轭自对偶表示的奇偶性

Parity of conjugate self-dual representations of inner forms of $\mathrm{GL}_n$ over $p$-adic fields

本文证明了共轭自对偶离散序列表示的 Langlands 参数奇偶性与 Jacquet-Langlands 像奇偶性之间的一般公式，推广了 Mieda 的部分结果并变体化了 Prasad-Ramakrishnan 的自对偶结果。

2022-04-19math.NTmath.RT

$p$-adic经典群与内形式的块分解

Block decompositions for $p$-adic classical groups and their inner forms

Imperial College（帝国理工学院）；University of Sheffield（谢菲尔德大学）；ShanghaiTech University（上海科技大学）；University of East Anglia（东英吉利大学）

研究通过内参数分解$p$-adic经典群及其内形式的光滑表示范畴，证明诱导保分解并建立块与内参数的自然双射。

2026-04-02math.NTmath.RT

比较 Bushnell-Kutzko 与 Sécherre 对 $\mathrm{GL}_{N}$ 及其内形式的类型构造与 Yu 的构造

Comparing Bushnell-Kutzko and Sécherre's constructions of types for $\mathrm{GL}_{N}$ and its inner forms with Yu's construction

本文比较了 Sécherre 的简单类型与 Yu 的构造在中心单代数乘法群超尖点表示类型上的关系，证明 Bushnell-Henniart 的本质驯服超尖点表示与 Yu 的驯服超尖点表示一致。

2024-07-01math.NTmath.RT

更多相关论文收起更多论文

关于内形式 $\mathrm{GL}_n$ 的 Braverman-Kazhdan 渐近 Hecke 代数

On Braverman-Kazhdan's asymptotic Hecke algebra for inner forms of $\mathrm{GL}_n$

School of Mathematics and Statistics, University of Glasgow（格拉斯哥大学数学与统计学院）

研究p-adic GL_n内形式G的Braverman-Kazhdan渐近Hecke代数J(G)，证明其在Q_ℓ上定义并适用于范畴局部Langlands对应，给出L-参数约化中心化子的显式公式，并证明J(G)与C_c^∞(G)有相同Hochschild同调。

2026-06-23math.NTmath.RT

局部非阿基米德域上$\n\thrm{GL}_n$内形式的模表示研究

On modular representations of inner forms of $\mathrm{GL}_n$ over a local non-archimedean field

该研究将局部非阿基米德域上$\n\thrm{GL}_n$内形式的$\nsquare$-不可约表示结果推广到模系数域，给出$L$-因子计算、分类穷举性新证明及抛物诱导表示成分刻画。

2024-09-15math.RT

Sally-Shalika 特征标公式与 $\mathrm{SL}_2$ 的内窥特征标恒等式的比较

Comparison of the Sally-Shalika character formulas with the endoscopic character identities for $\mathrm{SL}_2$

本文比较了 $\mathrm{SL}_2(F)$ 深度为零超尖 $L$-包的内窥特征标恒等式与 Sally-Shalika 经典公式，重点揭示大小为 $4$ 的 $L$-包中范数 $1$ 群 $H_1,H_2,H_3$ 的关键作用。

2025-10-23math.NTmath.RT

Gamma factors of intertwining periods and distinction for inner forms of $\mathrm{GL(n)}$

Let $F$ be a $p$-adic field, $E$ be a quadratic extension of $F$, $D$ be an $F$-central division algebra of odd index and let $θ$ be the Galois involution attached to $E/F$. Set $H=GL(m,D)$, $G=GL(m,D\otimes_F E)$, and let $P=MU$ be a standard parabolic subgroup of $G$. Let $w$ be a Weyl involution stabilizing $M$ and $M^{θ_w}$ be the subgroup of $M$ fixed by the involution $θ_w:m\mapsto θ(wmw)$. We denote by $X(M)^{w,-}$ the complex torus of $w$-anti-invariant unramified characters of $M$. Following the global methods of Jacquet, Lapid and Rogawski, we associate to a finite length representat…

2021-08-18math.NTmath.RT

Generalized Poincaré series for $\mathrm{SU}(2,1)$

We define and study 'non-abelian' Poincaré series for the group $G=\mathrm{SU} (2,1)$, i.e. Poincaré series attached to a Stone-Von Neumann representation of the unipotent subgroup $N$ of $G$. Such Poincaré series have in general exponential growth. In this study we use results on abelian and non-abelian Fourier term modules obtained in arXiv:1912.01334. We compute the inner product of truncations of these series and those associated to unitary characters of $N$ with square integrable automorphic forms, in connection with their Fourier expansions. As a consequence, we obtain general completene…

2021-09-30math.NTmath.RT

Fargues-Scholze与Gan-Takeda局部Langlands的兼容性

Compatibility of the Fargues-Scholze and Gan-Takeda Local Langlands

本文证明了在非分歧且p>2的条件下，Fargues-Scholze构造的半单Weil参数与Gan-Takeda关于GSp4及其非分裂内形式的局部Langlands对应相兼容，并利用局部Shimura簇上同调验证了Kottwitz猜想的强形式。

2026-10-08math.NTmath.RT

二维局部域上 GL_n×GL_n 的主系列 2-表示

The principal series 2-representation for $\mathrm{GL}_n\times\mathrm{GL}_n$ over a 2-dimensional local field

Westlake Institute for Advanced Study（西湖高等研究院）；Institute for Theoretical Sciences, Westlake University（西湖大学理论科学研究院）；Westlake University（西湖大学）

该研究构造了二维局部域上 GL_n×GL_n 的主系列 2-表示，通过交叉-$K_2$ 乘子与扭曲等变化实现，为非分歧结构提供了二维范畴类比。

2026-08-18math.NTmath.RT

GSp(4) 的内形式之间的整体提升

Global liftings between inner forms of GSp(4)

本文研究数域上约化群到其拟分裂内形式的自守提升，证明许多情形下非平凡上同调弱整体提升的存在性，并针对 GSp(4) 内形式解决局部提升的精细细节，证实了 Ibukiyama-Kitayama 关于平方自由水平参数模新形式的猜想。

2023-06-21math.NTmath.RT

Weil representations via abstract data and Heisenberg groups: a comparison

Let $B$ be a ring, not necessarily commutative, having an involution $*$ and let ${\mathrm U}_{2m}(B)$ be the unitary group of rank $2m$ associated to a hermitian or skew hermitian form relative to $*$. When $B$ is finite, we construct a Weil representation of ${\mathrm U}_{2m}(B)$ via Heisenberg groups and find its explicit matrix form on the Bruhat elements. As a consequence, we derive information on generalized Gauss sums. On the other hand, there is an axiomatic method to define a Weil representation of ${\mathrm U}_{2m}(B)$, and we compare the two Weil representations thus obtained under …

2019-06-08math.GRmath.RAmath.RT

Représentations modulo $p$ de $\mathrm{GL}(m,D)$, $D$ algèbre à division sur un corps local

This Ph.D. thesis belongs to the realm of mod $p$ representation theory of $p$-adic groups. The main object of study is the inner form of the general linear group $\mathrm{GL}(m,D)$ where $D$ is a division algebra over a non-Archimedean local field. The first part focuses on the rank $1$ case ($m=2$): it develops in detail the irreducibility criterion for parabolically induced representations and a classification of irreducible admissible smooth representations "à la Barthel-Livné". Then one turns to the generalized Steinberg representations: building on ideas of Grosse-Klönne and Herzig, this…

2014-09-16math.RT

Classification of balanced toral elements of exceptional Lie algebras

Let $\mathfrak{g}$ be a simple Lie algebra of exceptional type over an algebraically closed field $k$, and let $G$ be a simple linear algebraic group with Lie algebra $\mathfrak{g}$. For $\mathrm{char} \, k =p >0$, we present a complete classification of the $G$-conjugacy classes of balanced toral elements of $\mathfrak{g}$. As a result, we also obtain the classification of conjugacy classes of balanced inner torsion automorphisms of $\mathfrak{g}$ of order $p$ when $\mathrm{char} \, k =0$.

2018-08-24math.RT