Pub Date : 2018-07-15DOI: 10.1007/s11537-018-1803-1
Victor G. Kac, Johan W. van de Leur
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.
{"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}
Pub Date : 2018-03-01DOI: 10.1007/s11537-018-1640-2
A. Bourget, Allen Alvarez Loya, T. McMillen
{"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}
Pub Date : 2018-02-14DOI: 10.1007/s11537-017-1714-6
A. Kuznetsov, Yuri Prokhorov, C. Shramov
{"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}
Pub Date : 2017-11-30DOI: 10.1007/s11537-017-1622-9
K. Fukaya
{"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}
Pub Date : 2017-08-21DOI: 10.1007/s11537-017-1648-z
David A. Vogan
An infinite-dimensional representation π of a real reductive Lie group G can often be thought of as a function space on some manifold X. Although X 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 X. These invariants are easy to define but difficult to compute. I will describe some of the invariants, and recent progress toward computing them.
{"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}
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