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Loop and double loop geometry

环路和双环几何形状

基本信息

批准号：
19K14495
负责人：
MUTHIAH DINAKAR
金额：
$ 2.41万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Early-Career Scientists
财政年份：
2019
资助国家：
日本
起止时间：
2019-04-01 至 2024-03-31
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-19K14495/
关键词：
Coulomb branches KM Affine Grassmannians KM Affine Hecke Algebras Iwahori-Hecke algebras Monopole Operators Coulomb branch affine Grassmannian (double) loop groups affine Grassmannians Geometric Satake p-adic Kac-Moody groups bow var

项目摘要

One of the long term goals of this project is to better understand the Coulomb branches of quiver gauge theories, which give rise to a definition of Kac-Moody affine Grassmannian slices. Specifically the goal is to understand their geometry explicitly. In November 2022, my collaborator, Alex Weekes, and I posted a preprint titled "Fundamental monopole operators and embeddings of Kac-Moody affine Grassmannian slices". In this paper, we construct embeddings of Kac-Moody affine Grassmannian slices into one another using Fundamental Monopole Operators. In this way, we answer a question posed by Finkelberg in his 2018 address at the ICM (International Congress of Mathematicians). In particular, we are able to construct many Poisson subvarieties of Kac-Moody Affine Grassmannian slices in this way. Our hope is that the Fundamental Monopole Operators will be a crucial tool in further investigations of Kac-Moody Affine Grassmannian slices.Additionally, I have made further progress in the project with Auguste Hebert on understanding completions of Kac-Moody Affine Hecke algebras. I have also made progress in the project with Anna Puskas on the T-basis of Kac-Moody Affine Hecke algebras and its relationship with the length function and Bruhat order.

这个项目的长期目标之一是更好地理解箭图规范理论的库仑分支，它引起了Kac-Moody仿射Grassman切片的定义。具体地说，目标是明确了解它们的几何图形。2022年11月，我和我的合作者Alex Weekes发布了一本预印本，标题是《基本单极子算子和Kac-Moody仿射Grassmanian切片的嵌入》。本文利用基本单极算子构造了Kac-Moody仿射Grassman切片的相互嵌入。通过这种方式，我们回答了芬克尔伯格在2018年国际数学家大会(ICM)上发表演讲时提出的一个问题。特别地，我们可以用这种方法构造Kac-Moody仿射Grassman切片的许多Poisson亚簇。我们希望基本单极子算子将成为进一步研究Kac-Moody Affine Grassmanian切片的重要工具。此外，我与Auguste Hebert在理解Kac-Moody Affine Hecke代数的完备化方面取得了进一步的进展。我还与Anna Puskas在Kac-Moody Affine Hecke代数的T-基及其与长度函数和Bruhat序的关系方面取得了进展。

项目成果

期刊论文数量（16）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Toward double affine flag varieties and Grassmannians.

走向双仿射旗变种和格拉斯曼尼亚。

DOI：
发表时间：
2019
期刊：
影响因子：
0
作者：
Dinakar Muthiah;Anna Puskas;Ian Whitehead;Dinakar Muthiah;Dinakar Muthiah;Dinakar Muthiah;Dinakar Muthiah;Dinakar Muthiah;Dinakar Muthiah;Dinakar Muthiah
通讯作者：
Dinakar Muthiah

The equations defining affine Grassmannians in type A and a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman.

定义 A 型仿射格拉斯曼方程以及 Kreiman、Lakshmibai、Magyar 和 Weyman 的猜想。