Computation of matrix factorizations for discriminants of pseudo-reflection groups

伪反射群判别式的矩阵分解计算

• 批准号: NE/T014016/1
• 负责人: Eleonore Faber
• 金额: $ 0.74万
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=NE%2FT014016%2F1
• 关键词: Computation; matrix; factorizations; discriminants; pseudo

EPSRC : Simon May : EP/R513258/1This Globalink Research Placement should take place at Carleton University in the Autumn of 2020. It will allow the applicant Simon May to spend 12 weeks at the host university and complement the theoretical work in his Ph.D. thesis with explicit computations of matrix factorizations for discriminants of pseudo-reflection groups. It will also allow the applicant to take part in courses and research seminars at the host University in order to establish collaborations with the host supervisor and his group as well as to grow his professional network.The background for this work is the McKay correspondence, that relates three areas in pure mathematics: algebraic geometry, commuative algebra and representation theory of finite groups. Very recently, a McKay correspondence for reflection groups has been established, that relates irreducible representations of finite groups generated by reflections to certain modules over the coordinate rings of the discriminants of these reflection groups. These modules are maximal Cohen-Macaulay modules and can be described by so-called matrix factorizations.The goal of this project is to explicitly compute (in Macaulay2) matrix factorizations for discriminants of pseudo-reflection groups and so obtain insights that can lead to a better understanding of these objects.

EPSRC：Simon May：EP/R513258/1这个Globalink研究实习应该在2020年秋季在卡尔顿大学进行。它将允许申请人西蒙·梅在东道国大学度过12周，并补充他的博士理论工作。论文与显式计算矩阵分解的伪反射群的判别式。它还将允许申请人参加课程和研究研讨会在东道国大学，以建立与东道国主管和他的小组的合作，以及发展他的专业网络。背景这项工作是麦凯对应，涉及三个领域的纯数学：代数几何，交换代数和表示理论的有限群。最近，反射群的McKay对应已经建立，它将由反射生成的有限群的不可约表示与这些反射群的判别式的坐标环上的某些模块联系起来。这些模是极大的Cohen-Macaulay模，可以用所谓的矩阵分解来描述。这个项目的目标是显式地计算（在Macaulay 2中）伪反射群的判别式的矩阵分解，从而获得可以更好地理解这些对象的见解。