Letters in Mathematical Physics最新文献

Marginally outer trapped surface with capillary boundary and rigidity of initial data sets 具有毛细边界和初始数据集刚性的边缘外捕获表面

IF 1.6 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-10-17 DOI: 10.1007/s11005-026-02176-3

Sanghun Lee

引用次数: 0

BV pushforward of Palatini–Cartan gravity BV推进帕拉蒂尼-卡尔坦重力

IF 1.6 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-10-16 DOI: 10.1007/s11005-026-02149-6

Giovanni Canepa, Alberto S. Cattaneo

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Classifying integral Grothendieck rings up to rank 5 and beyond 分类积分Grothendieck环可达5级及以上

IF 1.6 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-10-15 DOI: 10.1007/s11005-026-02164-7

Max A. Alekseyev, Winfried Bruns, Jingcheng Dong, Sebastien Palcoux

{"title":"Classifying integral Grothendieck rings up to rank 5 and beyond","authors":"Max A. Alekseyev, Winfried Bruns, Jingcheng Dong, Sebastien Palcoux","doi":"10.1007/s11005-026-02164-7","DOIUrl":"10.1007/s11005-026-02164-7","url":null,"abstract":"<div>In this paper, we define a Grothendieck ring as a fusion ring categorifiable into a fusion category over the complex field. An integral fusion ring is called Drinfeld if all its formal codegrees are integers dividing the global Frobenius–Perron dimension. Every integral Grothendieck ring is necessarily Drinfeld. Using the fact that the formal codegrees of integral Drinfeld rings form an Egyptian fraction summing to 1, we derive a finite list of candidate global FPdims for small ranks, covering all that occur. Using Normaliz (an open-source software for computing algebraic polyhedra), we classify all integral fusion rings with these candidate FPdims, retaining only those admitting a Drinfeld structure. To exclude Drinfeld rings that are not Grothendieck rings, we analyze induction matrices to the Drinfeld center, classified via our new feature on Normaliz. Further exclusions and constructions involve group-theoretical fusion categories and Schur multipliers. Our main result is a complete classification of integral Grothendieck rings up to rank 5, extended to rank 7 in odd-dimensional and noncommutative cases using Frobenius–Schur indicators and Galois theory. Moreover, we show that any noncommutative, odd-dimensional, integral Grothendieck ring of rank at most 22 is pointed of rank 21. We also classify all integral 1-Frobenius Drinfeld rings of rank 6, identify the first known non-Isaacs integral fusion category (which turns out to be group-theoretical), and classify integral noncommutative Drinfeld rings of rank 8 and integral 1-Frobenius MNSD Drinfeld rings of rank 9. Finally, we determine the smallest rank simple exotic integral fusion rings: rank 4 in general, rank 6 in the Drinfeld case, and rank 7 in the 1-Frobenius Drinfeld case.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Actions of Lie 2-algebras and comomentum maps 李2 -代数的作用与评论映射

IF 1.6 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-10-14 DOI: 10.1007/s11005-026-02154-9

Philippe Bonneau, Véronique Chloup, Angela Gammella-Mathieu, Tilmann Wurzbacher

{"title":"Actions of Lie 2-algebras and comomentum maps","authors":"Philippe Bonneau, Véronique Chloup, Angela Gammella-Mathieu, Tilmann Wurzbacher","doi":"10.1007/s11005-026-02154-9","DOIUrl":"10.1007/s11005-026-02154-9","url":null,"abstract":"<div>In this article we first introduce the notion of a 2-action of a Lie 2-algebra on an arbitrary manifold M. C.L. Rogers associates in [10] a (L_{infty })-algebra (mathsf {L^{infty }(M,omega )}) to a n-plectic manifold ((M,omega )), as a higher analogue of the Poisson algebra of observables associated to a symplectic manifold. This (L_{infty })-algebra reduces to a Lie 2-algebra (mathsf {L^2(M,omega )}) when ((M,omega )) is 2-plectic. Following ideas of N.L. Delgado (cf. [4]), we introduce the Lie 2-algebra (mathsf {D^2(M,omega )}), which generalises the Lie 2-algebra (textsf{L}^2(M,omega )), and its extension (mathsf {widetilde{D^2(M,omega )}}) containing Hamiltonian pairs. Given a 2-plectic manifold ((M,omega )) and a Lie 2-algebra (mathfrak {g}_{-1}oplus mathfrak {g}_{0}) acting on M we define a comomentum map as a lift of the action, i.e., as a Lie 2-algebra morphism from (mathfrak {g}_{-1}oplus mathfrak {g}_{0}) to the Lie 2-algebra (mathsf {widetilde{D^2(M,omega )}}). In an appendix, we discuss very explicitly numerous examples, classified according to their algebraic properties.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Infinite-dimensional representations of (U_q(mathfrak {sl}_2)) and the shadow world: quantum 6j-symbols for Verma modules (U_q(mathfrak {sl}_2))的无限维表示和影子世界：Verma模块的量子6j符号

IF 1.6 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-10-14 DOI: 10.1007/s11005-026-02133-0

Dmitry Solovyev

引用次数: 0

A (3times 3) linear q-difference system with (E_8^{(1)})-symmetry 具有(E_8^{(1)}) -对称的(3times 3)线性q差系统

IF 1.6 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-10-11 DOI: 10.1007/s11005-026-02161-w

Takahiko Nobukawa

{"title":"A (3times 3) linear q-difference system with (E_8^{(1)})-symmetry","authors":"Takahiko Nobukawa","doi":"10.1007/s11005-026-02161-w","DOIUrl":"10.1007/s11005-026-02161-w","url":null,"abstract":"<div>We present a linear q-difference equation of rank 3, which admits the affine Weyl group symmetry of type (E_8^{(1)}). This equation has essentially 8 parameters and 2 accessory parameters. We characterize this equation by the spectral type of q-difference system which is introduced by Sakai–Yamaguchi. We further compare this equation with Moriyama–Yamada’s quantum curve which has (W(E_8^{(1)}))-symmetry. We show that our equation can be regarded as an extension of Moriyama–Yamada’s curve. We introduce the point configuration of a higher-order scalar q-difference equation to characterize our equation and clarify the corresponding between our equation and the curve. The symmetry of our equation is provided by the q-middle convolution, defined by Sakai–Yamaguchi and reformulated by Arai–Takemura. In this paper, we provide a reconstruction of the q-middle convolution via a q-Okubo-type equation. This construction is a natural q-analog of the middle convolution of Fuchsian differential equation. Several properties for our q-middle convolution are also discussed.\u0000</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02161-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The continuum limit analysis of causal fermion systems for curved spacetimes 弯曲时空下因果费米子系统的连续统极限分析

IF 1.6 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-10-09 DOI: 10.1007/s11005-026-02168-3

Felix Finster, Patrick Fischer

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On the partial semi-classical Weyl’s law 关于部分半经典Weyl定律

IF 1.6 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-10-09 DOI: 10.1007/s11005-026-02173-6

Younghun Hong, Sangdon Jin

引用次数: 0

On singular solitons of the KP equation and the Go-diagrams 关于KP方程和go图的奇异孤子

IF 1.6 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-10-08 DOI: 10.1007/s11005-026-02172-7

Shilong Huang

引用次数: 0

Spectral structure of the mixed Hessian of the dispersionless Toda (tau )-function 无色散Toda函数的混合Hessian谱结构(tau ) -函数

IF 1.6 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-10-06 DOI: 10.1007/s11005-026-02170-9

Oleg Alekseev

{"title":"Spectral structure of the mixed Hessian of the dispersionless Toda (tau )-function","authors":"Oleg Alekseev","doi":"10.1007/s11005-026-02170-9","DOIUrl":"10.1007/s11005-026-02170-9","url":null,"abstract":"<div>We study the mixed Hessian of the dispersionless Toda (tau )-function for the one-harmonic (s)-fold symmetric conformal map (f(w)=rbigl (w+zeta w^{1-s}bigr )), where (r>0) is the exterior conformal radius and (zeta >0) is the dimensionless shape parameter. This Hessian is the susceptibility matrix generated by the inverse conformal map. Our spectral statements are formulated for its weighted symmetry-block realizations on a fixed Hilbert space. In that realization, the first spectral transition occurs at the analytic threshold (zeta _c=(s-1)^{s-1}/s^s), where the dominant square-root singularity of the inverse map reaches the circle (|z|=r), rather than at the geometric threshold (zeta _{textrm{univ}}=1/(s-1)), where univalence fails. After symmetry decomposition and weighted realization, each block develops exactly one logarithmically diverging eigenvalue as (zeta uparrow zeta _c), while the remaining spectrum stays bounded and converges to a compact limit. The instability is therefore rank one in every symmetry sector of the weighted block theory. We then continue the scalar Gram generating functions beyond (zeta _c). They are generalized hypergeometric functions on the slit plane (mathbb {C}{setminus }[zeta _c^2,infty )), their branch-point expansion contains the logarithmic term responsible for the divergence, and in the range (1le ple s) they admit Cauchy–Stieltjes and Jacobi-matrix realizations. In particular, the continued scalar quantities remain regular at (zeta _{textrm{univ}}), so the analytic spectral transition strictly precedes the geometric breakdown of univalence.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0