Vershik-Kerov 极限形状的椭圆类似物

IF 0.6 4区数学 Q3 MATHEMATICS Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI:10.1134/S0016266324020059

Andrei Grekov, Nikita Nekrasov

{"title":"Vershik-Kerov 极限形状的椭圆类似物","authors":"Andrei Grekov, Nikita Nekrasov","doi":"10.1134/S0016266324020059","DOIUrl":null,"url":null,"abstract":" We review the limit shape problem for the Plancherel measure and its generalizations found in supersymmetric gauge theory instanton count. We focus on the measure, interpolating between the Plancherel measure and the uniform measure, a \\(U(1)\\) case of \\(\\mathcal{N}=2^{*}\\) gauge theory. We give the formula for its limit shape in terms of elliptic functions, generalizing the trigonometric “arcsin” law of Vershik–Kerov and Logan–Schepp. ","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S0016266324020059.pdf","citationCount":"0","resultStr":"{\"title\":\"Elliptic Analogue of the Vershik–Kerov Limit Shape\",\"authors\":\"Andrei Grekov, Nikita Nekrasov\",\"doi\":\"10.1134/S0016266324020059\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" We review the limit shape problem for the Plancherel measure and its generalizations found in supersymmetric gauge theory instanton count. We focus on the measure, interpolating between the Plancherel measure and the uniform measure, a \\\\(U(1)\\\\) case of \\\\(\\\\mathcal{N}=2^{*}\\\\) gauge theory. We give the formula for its limit shape in terms of elliptic functions, generalizing the trigonometric “arcsin” law of Vershik–Kerov and Logan–Schepp. \",\"PeriodicalId\":575,\"journal\":{\"name\":\"Functional Analysis and Its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1134/S0016266324020059.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Functional Analysis and Its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0016266324020059\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Functional Analysis and Its Applications","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S0016266324020059","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要我们回顾了普朗切尔量度的极限形状问题及其在超对称规理论瞬子计数中的泛化。我们关注的是介于普朗切尔量度和均匀量度之间的量度，它是\(\mathcal{N}=2^{*}\)规理论的一种(U(1)\)情况。我们用椭圆函数给出了它的极限形状公式，概括了 Vershik-Kerov 和 Logan-Schepp 的三角函数 "arcsin "定律。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Elliptic Analogue of the Vershik–Kerov Limit Shape

We review the limit shape problem for the Plancherel measure and its generalizations found in supersymmetric gauge theory instanton count. We focus on the measure, interpolating between the Plancherel measure and the uniform measure, a \(U(1)\) case of \(\mathcal{N}=2^{*}\) gauge theory. We give the formula for its limit shape in terms of elliptic functions, generalizing the trigonometric “arcsin” law of Vershik–Kerov and Logan–Schepp.

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

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.