Symmetry Integrability and Geometry-Methods and Applications最新文献_第7页

Deformations of Instanton Metrics 瞬变子度量的变形

IF 0.9 3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-08-31 DOI: 10.3842/SIGMA.2023.041

R. Bielawski, Yannic Borchard, Sergey A. Cherkis

引用次数: 1

Separation of Variables and Superintegrability on Riemannian Coverings 黎曼覆盖上的变量分离与超可积性

IF 0.9 3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-08-26 DOI: 10.3842/SIGMA.2023.062

C. Chanu, G. Rastelli

引用次数: 0

Law of Large Numbers for Roots of Finite Free Multiplicative Convolution of Polynomials 多项式有限自由乘法卷积根的大数定律

IF 0.9 3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-08-24 DOI: 10.3842/SIGMA.2023.004

Katsunori Fujie, Yuki Ueda

引用次数: 0

From pp-Waves to Galilean Spacetimes 从pp波到伽利略时空

IF 0.9 3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-08-16 DOI: 10.3842/SIGMA.2023.035

J. Figueroa-O’Farrill, Ross Grassie, Stefan Prohazka

引用次数: 2

Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points 点的Hilbert格式上的大和Nef同义向量束

IF 0.9 3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-08-12 DOI: 10.3842/SIGMA.2022.061

D. Oprea

引用次数: 3

On Asymptotically Locally Hyperbolic Metrics with Negative Mass 关于负质量的渐近局部双曲度量

IF 0.9 3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-07-29 DOI: 10.3842/SIGMA.2023.005

Piotr T. Chru'sciel, E. Delay

引用次数: 1

Topology of Almost Complex Structures on Six-Manifolds 六流形上几乎复杂结构的拓扑

IF 0.9 3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-07-26 DOI: 10.3842/SIGMA.2022.093

Gustavo Granja, A. Milivojević

引用次数: 0

Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Parseval-Plancherel-Type Formulas under Subgroups 有界对称域上加权Bergman内积的计算及子群下的Parseval Plancherel型公式

IF 0.9 3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-07-24 DOI: 10.3842/SIGMA.2023.049

Ryosuke Nakahama

{"title":"Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Parseval-Plancherel-Type Formulas under Subgroups","authors":"Ryosuke Nakahama","doi":"10.3842/SIGMA.2023.049","DOIUrl":"https://doi.org/10.3842/SIGMA.2023.049","url":null,"abstract":"Let $(G,G_1)=(G,(G^sigma)_0)$ be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces $D_1=G_1/K_1subset D=G/K$, realized as bounded symmetric domains in complex vector spaces ${mathfrak p}^+_1:=({mathfrak p}^+)^sigmasubset{mathfrak p}^+$ respectively. Then the universal covering group $widetilde{G}$ of $G$ acts unitarily on the weighted Bergman space ${mathcal H}_lambda(D)subset{mathcal O}(D)={mathcal O}_lambda(D)$ on $D$ for sufficiently large $lambda$. Its restriction to the subgroup $widetilde{G}_1$ decomposes discretely and multiplicity-freely, and its branching law is given explicitly by Hua-Kostant-Schmid-Kobayashi's formula in terms of the $widetilde{K}_1$-decomposition of the space ${mathcal P}({mathfrak p}^+_2)$ of polynomials on ${mathfrak p}^+_2:=({mathfrak p}^+)^{-sigma}subset{mathfrak p}^+$. The object of this article is to understand the decomposition of the restriction ${mathcal H}_lambda(D)|_{widetilde{G}_1}$ by studying the weighted Bergman inner product on each $widetilde{K}_1$-type in ${mathcal P}({mathfrak p}^+_2)subset{mathcal H}_lambda(D)$. For example, by computing explicitly the norm $Vert fVert_lambda$ for $f=f(x_2)in{mathcal P}({mathfrak p}^+_2)$, we can determine the Parseval-Plancherel-type formula for the decomposition of ${mathcal H}_lambda(D)|_{widetilde{G}_1}$. Also, by computing the poles of $langle f(x_2),{rm e}^{(x|overline{z})_{{mathfrak p}^+}}rangle_{lambda,x}$ for $f(x_2)in{mathcal P}({mathfrak p}^+_2)$, $x=(x_1,x_2)$, $zin{mathfrak p}^+={mathfrak p}^+_1oplus{mathfrak p}^+_2$, we can get some information on branching of ${mathcal O}_lambda(D)|_{widetilde{G}_1}$ also for $lambda$ in non-unitary range. In this article we consider these problems for all $widetilde{K}_1$-types in ${mathcal P}({mathfrak p}^+_2)$.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47841101","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

A Novel Potential Featuring Off-Center Circular Orbits 一种具有偏心圆轨道的新势

IF 0.9 3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-07-20 DOI: 10.3842/SIGMA.2023.001

M. Olshanii

引用次数: 1

Complementary Modules of Weierstrass Canonical Forms Weierstrass规范形式的互补模

IF 0.9 3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-07-05 DOI: 10.3842/SIGMA.2022.098

J. Komeda, S. Matsutani, E. Previato

{"title":"Complementary Modules of Weierstrass Canonical Forms","authors":"J. Komeda, S. Matsutani, E. Previato","doi":"10.3842/SIGMA.2022.098","DOIUrl":"https://doi.org/10.3842/SIGMA.2022.098","url":null,"abstract":"The Weierstrass curve is a pointed curve $(X,infty)$ with a numerical semigroup $H_X$, which is a normalization of the curve given by the Weierstrass canonical form, $y^r + A_{1}(x) y^{r-1} + A_{2}(x) y^{r-2} +dots + A_{r-1}(x) y + A_{r}(x)=0$ where each $A_j$ is a polynomial in $x$ of degree $leq j s/r$ for certain coprime positive integers $r$ and $s$, $r$<$s$, such that the generators of the Weierstrass non-gap sequence $H_X$ at $infty$ include $r$ and $s$. The Weierstrass curve has the projection $varpi_rcolon X to {mathbb P}$, $(x,y)mapsto x$, as a covering space. Let $R_X := {mathbf H}^0(X, {mathcal O}_X(*infty))$ and $R_{mathbb P} := {mathbf H}^0({mathbb P}, {mathcal O}_{mathbb P}(*infty))$ whose affine part is ${mathbb C}[x]$. In this paper, for every Weierstrass curve $X$, we show the explicit expression of the complementary module $R_X^{mathfrak c}$ of $R_{mathbb P}$-module $R_X$ as an extension of the expression of the plane Weierstrass curves by Kunz. The extension naturally leads the explicit expressions of the holomorphic one form except $infty$, ${mathbf H}^0({mathbb P}, {mathcal A}_{mathbb P}(*infty))$ in terms of $R_X$. Since for every compact Riemann surface, we find a Weierstrass curve that is bi-rational to the surface, we also comment that the explicit expression of $R_X^{mathfrak c}$ naturally leads the algebraic construction of generalized Weierstrass' sigma functions for every compact Riemann surface and is also connected with the data on how the Riemann surface is embedded into the universal Grassmannian manifolds.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48355842","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: 4