最小格尔芬-基里洛夫维度的 GLn(ℂ) 不可还原表征

IF 0.8 3区数学 Q2 MATHEMATICS Acta Mathematica Sinica-English Series Pub Date : 2024-03-15 DOI:10.1007/s10114-024-3207-x

Zhan Qiang Bai, Yang Yang Chen, Dong Wen Liu, Bin Yong Sun

{"title":"最小格尔芬-基里洛夫维度的 GLn(ℂ) 不可还原表征","authors":"Zhan Qiang Bai, Yang Yang Chen, Dong Wen Liu, Bin Yong Sun","doi":"10.1007/s10114-024-3207-x","DOIUrl":null,"url":null,"abstract":"<div>In this article, by studying the Bernstein degrees and Goldie rank polynomials, we establish a comparison between the irreducible representations of G = GLn(ℂ) possessing the minimal Gelfand–Kirillov dimension and those induced from finite-dimensional representations of the maximal parabolic subgroup of G of type (n − 1,1). We give the transition matrix between the two bases for the corresponding coherent families.</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 3","pages":"639 - 657"},"PeriodicalIF":0.8000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Irreducible Representations of GLn(ℂ) of Minimal Gelfand–Kirillov Dimension\",\"authors\":\"Zhan Qiang Bai, Yang Yang Chen, Dong Wen Liu, Bin Yong Sun\",\"doi\":\"10.1007/s10114-024-3207-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>In this article, by studying the Bernstein degrees and Goldie rank polynomials, we establish a comparison between the irreducible representations of G = GLn(ℂ) possessing the minimal Gelfand–Kirillov dimension and those induced from finite-dimensional representations of the maximal parabolic subgroup of G of type (n − 1,1). We give the transition matrix between the two bases for the corresponding coherent families.</div>\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":\"40 3\",\"pages\":\"639 - 657\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Sinica-English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10114-024-3207-x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-024-3207-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，通过研究伯恩斯坦度和戈尔迪秩多项式，我们建立了 G = GLn(ℂ)具有最小格尔芬-基里洛夫维度的不可还原表示与 G 的最大抛物面子群类型（n - 1,1）的有限维表示所诱导的不可还原表示之间的比较。我们给出了相应相干族的两个基之间的转换矩阵。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Irreducible Representations of GLn(ℂ) of Minimal Gelfand–Kirillov Dimension

In this article, by studying the Bernstein degrees and Goldie rank polynomials, we establish a comparison between the irreducible representations of G = GL_n(ℂ) possessing the minimal Gelfand–Kirillov dimension and those induced from finite-dimensional representations of the maximal parabolic subgroup of G of type (n − 1,1). We give the transition matrix between the two bases for the corresponding coherent families.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.