{"title":"Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions","authors":"Victor G. Kac, Johan W. van de Leur","doi":"10.1007/s11537-018-1803-1","DOIUrl":"https://doi.org/10.1007/s11537-018-1803-1","url":null,"abstract":"We show that a system of Hirota bilinear equations introduced by Jimbo and Miwa defines tau-functions of the modified KP (MKP) hierarchy of evolution equations introduced by Dickey. Some other equivalent definitions of the MKP hierarchy are established. All polynomial tau-functions of the KP and the MKP hierarchies are found. Similar results are obtained for the reduced KP and MKP hierarchies.","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"134 ","pages":"235-271"},"PeriodicalIF":1.5,"publicationDate":"2018-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spectral asymptotics for Kac–Murdock–Szegő matrices","authors":"A. Bourget, Allen Alvarez Loya, T. McMillen","doi":"10.1007/s11537-018-1640-2","DOIUrl":"https://doi.org/10.1007/s11537-018-1640-2","url":null,"abstract":"","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"13 1","pages":"67 - 107"},"PeriodicalIF":1.5,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11537-018-1640-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46031424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hilbert schemes of lines and conics and automorphism groups of Fano threefolds","authors":"A. Kuznetsov, Yuri Prokhorov, C. Shramov","doi":"10.1007/s11537-017-1714-6","DOIUrl":"https://doi.org/10.1007/s11537-017-1714-6","url":null,"abstract":"","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"13 1","pages":"109 - 185"},"PeriodicalIF":1.5,"publicationDate":"2018-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11537-017-1714-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49186469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Categorification of invariants in gauge theory and symplectic geometry","authors":"K. Fukaya","doi":"10.1007/s11537-017-1622-9","DOIUrl":"https://doi.org/10.1007/s11537-017-1622-9","url":null,"abstract":"","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"13 1","pages":"1 - 65"},"PeriodicalIF":1.5,"publicationDate":"2017-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11537-017-1622-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53189521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The size of infinite-dimensional representations","authors":"David A. Vogan","doi":"10.1007/s11537-017-1648-z","DOIUrl":"https://doi.org/10.1007/s11537-017-1648-z","url":null,"abstract":"An infinite-dimensional representation π of a real reductive Lie group <i>G</i> can often be thought of as a function space on some manifold <i>X</i>. Although <i>X</i> is not uniquely defined by π, there are “geometric invariants” of π, first introduced by Roger Howe in the 1970s, related to the geometry of <i>X</i>. These invariants are easy to define but difficult to compute. I will describe some of the invariants, and recent progress toward computing them.","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"136 ","pages":"175-210"},"PeriodicalIF":1.5,"publicationDate":"2017-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}