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Dirac series of E7(7) E7(7) 的狄拉克级数
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-09-03 DOI: 10.1007/s11856-024-2658-1
Yi-Hao Ding, Chao-Ping Dong, Lin Wei
{"title":"Dirac series of E7(7)","authors":"Yi-Hao Ding, Chao-Ping Dong, Lin Wei","doi":"10.1007/s11856-024-2658-1","DOIUrl":"https://doi.org/10.1007/s11856-024-2658-1","url":null,"abstract":"<p>This paper classifies all the Dirac series (that is, irreducible unitary representations having non-zero Dirac cohomology) of <i>E</i><sub>7(7)</sub>. Enhancing the Helgason–Johnson bound in 1969 for the group <i>E</i><sub>7(7)</sub> is one key ingredient. Our calculation partially supports Vogan’s fundamental parallelepiped (FPP) conjecture. As applications, when passing to Dirac index, we continue to find cancellation between the even part and the odd part of Dirac cohomology. Moreover, for the first time, we find Dirac series whose spin lowest <i>K</i>-types have multiplicities.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strong ergodicity around countable products of countable equivalence relations 围绕可数等价关系的可数乘积的强遍历性
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-09-03 DOI: 10.1007/s11856-024-2654-5
Assaf Shani
{"title":"Strong ergodicity around countable products of countable equivalence relations","authors":"Assaf Shani","doi":"10.1007/s11856-024-2654-5","DOIUrl":"https://doi.org/10.1007/s11856-024-2654-5","url":null,"abstract":"<p>This paper deals with countable products of countable Borel equivalence relations and equivalence relations “just above” those in the Borel reducibility hierarchy. We show that if <i>E</i> is strongly ergodic with respect to <i>μ</i> then <i>E</i><sup>ℕ</sup> is strongly ergodic with respect to <i>μ</i><sup>ℕ</sup>. We answer questions of Clemens and Coskey regarding their recently defined Γ-jump operations, in particular showing that the ℤ<sup><i>k</i>+1</sup>-jump of <i>E</i><sub>∞</sub> is strictly above the ℤ<sup><i>k</i></sup>-jump of <i>E</i><sub>∞</sub>. We study a notion of equivalence relations which can be classified by infinite sequences of “definably countable sets”. In particular, we define an interesting example of such an equivalence relation which is strictly above <i>E</i><span>\u0000<sup>ℕ</sup><sub>∞</sub>\u0000</span>, strictly below =<sup>+</sup>, and is incomparable with the Γ-jumps of countable equivalence relations.</p><p>We establish a characterization of strong ergodicity between Borel equivalence relations in terms of symmetric models, using results from [Sha21]. The proofs then rely on a fine analysis of the very weak choice principles “every sequence of <i>E</i>-classes admits a choice sequence”, for various countable Borel equivalence relations <i>E</i>.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algebras with superautomorphism: simple algebras and codimension growth 具有超同构性的代数：简单代数与维数增长
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-09-03 DOI: 10.1007/s11856-024-2663-4
Antonio Ioppolo, Daniela La Mattina
{"title":"Algebras with superautomorphism: simple algebras and codimension growth","authors":"Antonio Ioppolo, Daniela La Mattina","doi":"10.1007/s11856-024-2663-4","DOIUrl":"https://doi.org/10.1007/s11856-024-2663-4","url":null,"abstract":"<p>Let <i>A</i> be an associative algebra endowed with a superautomorphism <i>φ</i>. In this paper we completely classify the finite-dimensional simple algebras with superautomorphism of order ≤ 2. Moreover, after generalizing the Wedderburn–Malcev Theorem in this setting, we prove that the sequence of <i>φ</i>-codimensions of <i>A</i> is polynomially bounded if and only if the variety generated by <i>A</i> does not contain the group algebra of ℤ<sub>2</sub> and the algebra of 2 × 2 upper triangular matrices with suitable superautomorphisms.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The set of trace ideals of curve singularities 曲线奇点的迹理想集合
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-09-03 DOI: 10.1007/s11856-024-2661-6
Toshinori Kobayashi, Shinya Kumashiro
{"title":"The set of trace ideals of curve singularities","authors":"Toshinori Kobayashi, Shinya Kumashiro","doi":"10.1007/s11856-024-2661-6","DOIUrl":"https://doi.org/10.1007/s11856-024-2661-6","url":null,"abstract":"<p>We investigate a problem of when commutative local domains have a finite number of trace ideals. The problem is left for the case of dimension one. In this paper, with a necessary assumption, we give a complete answer by using integrally closed ideals. We also explore properties of such domains related to birational extensions, reflexive ideals, and reflexive Ulrich modules. Special attention is given in the case of numerical semigroup rings of non-gap four. We then obtain a criterion for a ring to have a finite number of reflexive ideals up to isomorphism. Non-domains arising from fiber products are also explored.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The suspension of a 4-manifold and its applications 四曲面的悬浮及其应用
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-09-03 DOI: 10.1007/s11856-024-2659-0
Tseleung So, Stephen Theriault
{"title":"The suspension of a 4-manifold and its applications","authors":"Tseleung So, Stephen Theriault","doi":"10.1007/s11856-024-2659-0","DOIUrl":"https://doi.org/10.1007/s11856-024-2659-0","url":null,"abstract":"<p>Let <i>M</i> be a smooth, orientable, closed, connected 4-manifold and suppose that <i>H</i><sub>1</sub>(<i>M</i>; ℤ) is finitely generated and has no 2-torsion. We give a homotopy decomposition of the suspension of <i>M</i> in terms of spheres, Moore spaces and Σℂ<i>P</i><sup>2</sup>. This is used to calculate any reduced generalized cohomology theory of <i>M</i> as a group and to determine the homotopy types of certain current groups and gauge groups.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rational maps and K3 surfaces 有理映射和 K3 表面
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-09-03 DOI: 10.1007/s11856-024-2656-3
Ilya Karzhemanov, Grisha Konovalov
{"title":"Rational maps and K3 surfaces","authors":"Ilya Karzhemanov, Grisha Konovalov","doi":"10.1007/s11856-024-2656-3","DOIUrl":"https://doi.org/10.1007/s11856-024-2656-3","url":null,"abstract":"<p>For a very general complex projective K3 surface <i>S</i> and a smooth projective surface <i>A</i> with trivial canonical class, we prove that there is no dominant rational map <i>A → S</i>, which is not an isomorphism.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Property (τ) in positive characteristic 正特征中的性质 (τ)
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-09-03 DOI: 10.1007/s11856-024-2660-7
Amir Mohammadi, Nattalie Tamam
{"title":"Property (τ) in positive characteristic","authors":"Amir Mohammadi, Nattalie Tamam","doi":"10.1007/s11856-024-2660-7","DOIUrl":"https://doi.org/10.1007/s11856-024-2660-7","url":null,"abstract":"<p>We prove a quantitative equidistribution statement for certain adelic homogeneous subsets in positive characteristic. As an application, we describe a proof of property (<i>τ</i>) for arithmetic groups in this context.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unique ergodicity of horocyclic flows on nonpositively curved surfaces 非正曲线表面上角环流的唯一遍历性
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-09-03 DOI: 10.1007/s11856-024-2662-5
Sergi Burniol Clotet
{"title":"Unique ergodicity of horocyclic flows on nonpositively curved surfaces","authors":"Sergi Burniol Clotet","doi":"10.1007/s11856-024-2662-5","DOIUrl":"https://doi.org/10.1007/s11856-024-2662-5","url":null,"abstract":"<p>On the unit tangent bundle of a nonflat compact nonpositively curved surface, we prove that there is a unique probability Borel measure invariant by a horocyclic flow which gives full measure to the set of rank 1 vectors recurrent by the geodesic flow. If we assume in addition that the surface has no flat strips, we show that the horocyclic flow is uniquely ergodic. These results are valid for any parametrization of the horocyclic flow.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimal ∗-varieties and superinvolutions 最小∗变量和超旋回
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-09-03 DOI: 10.1007/s11856-024-2657-2
Onofrio M. Di Vincenzo, Vincenzo C. Nardozza
{"title":"Minimal ∗-varieties and superinvolutions","authors":"Onofrio M. Di Vincenzo, Vincenzo C. Nardozza","doi":"10.1007/s11856-024-2657-2","DOIUrl":"https://doi.org/10.1007/s11856-024-2657-2","url":null,"abstract":"<p>We introduce a class of finite-dimensional superalgebras over an algebraically closed field of characteristic zero, whose Grassmann envelopes generate all ∗-minimal varieties. Moreover, we prove that any affine minimal variety of superalgebras with superinvolution is generated by a suitable element in this selected class.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Join operation for the Bruhat order and Verma modules 布鲁哈特阶和维尔马模块的连接操作
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2637-6
Hankyung Ko, Volodymyr Mazorchuk, Rafael Mrđen
{"title":"Join operation for the Bruhat order and Verma modules","authors":"Hankyung Ko, Volodymyr Mazorchuk, Rafael Mrđen","doi":"10.1007/s11856-024-2637-6","DOIUrl":"https://doi.org/10.1007/s11856-024-2637-6","url":null,"abstract":"<p>We observe that the join operation for the Bruhat order on a Weyl group agrees with the intersections of Verma modules in type <i>A</i>. The statement is not true in other types, and we propose a weaker correspondence. Namely, we introduce distinguished subsets of the Weyl group on which the join operation conjecturally agrees with the intersections of Verma modules. We also relate our conjecture with a statement about the socles of the cokernels of inclusions between Verma modules. The latter determines the first Ext space between a simple module and a Verma module. We give a conjectural complete description of such socles which we verify in a number of cases. Along the way, we determine the poset structure of the join-irreducible elements in Weyl groups and obtain closed formulae for certain families of Kazhdan–Lusztig polynomials.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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