Remark on the distributions supported on the nilpotent cone

Hengfei Lu

doi:10.1016/j.jalgebra.2025.03.044

Remark on the distributions supported on the nilpotent cone

Hengfei Lu

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Let F be a local field of characteristic zero. This note gives two examples for the vanishing of certain distributions supported on the nilpotent cone. Then we give a shorter proof to the multiplicity one theorem for the symmetric variety GL_n(D)/GL_n(E) where D is a 4-dimensional quaternion algebra over F and E is a quadratic field extension of F.

Original language	English
Pages (from-to)	139-158
Number of pages	20
Journal	Journal of Algebra
Volume	677
DOIs	https://doi.org/10.1016/j.jalgebra.2025.03.044
State	Published - 1 Sep 2025

Keywords

Coisotropic variety
D-modules
Distinction problems
Invariant tempered generalized functions

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10.1016/j.jalgebra.2025.03.044

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title = "Remark on the distributions supported on the nilpotent cone",

abstract = "Let F be a local field of characteristic zero. This note gives two examples for the vanishing of certain distributions supported on the nilpotent cone. Then we give a shorter proof to the multiplicity one theorem for the symmetric variety GLn(D)/GLn(E) where D is a 4-dimensional quaternion algebra over F and E is a quadratic field extension of F.",

keywords = "Coisotropic variety, D-modules, Distinction problems, Invariant tempered generalized functions",

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N2 - Let F be a local field of characteristic zero. This note gives two examples for the vanishing of certain distributions supported on the nilpotent cone. Then we give a shorter proof to the multiplicity one theorem for the symmetric variety GLn(D)/GLn(E) where D is a 4-dimensional quaternion algebra over F and E is a quadratic field extension of F.

AB - Let F be a local field of characteristic zero. This note gives two examples for the vanishing of certain distributions supported on the nilpotent cone. Then we give a shorter proof to the multiplicity one theorem for the symmetric variety GLn(D)/GLn(E) where D is a 4-dimensional quaternion algebra over F and E is a quadratic field extension of F.

KW - Coisotropic variety

KW - D-modules

KW - Distinction problems

KW - Invariant tempered generalized functions

UR - https://www.scopus.com/pages/publications/105002920702

U2 - 10.1016/j.jalgebra.2025.03.044

DO - 10.1016/j.jalgebra.2025.03.044

M3 - 文章

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SN - 0021-8693

VL - 677

SP - 139

EP - 158

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Remark on the distributions supported on the nilpotent cone

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Keywords

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