Transformation Groups最新文献

{"title":"Compact Hyperbolic Coxeter Five-Dimensional Polytopes with Nine Facets","authors":"Jiming Ma, Fangting Zheng","doi":"10.1007/s00031-023-09830-3","DOIUrl":"https://doi.org/10.1007/s00031-023-09830-3","url":null,"abstract":"<p>In this paper, we obtain a complete classification of compact hyperbolic Coxeter five-dimensional polytopes with nine facets.</p>","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138567876","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 Limit Set for Representations of Discrete Subgroups of $$text {PU}(1,n)$$ by the Plücker Embedding","authors":"Haremy Zuñiga","doi":"10.1007/s00031-023-09829-w","DOIUrl":"https://doi.org/10.1007/s00031-023-09829-w","url":null,"abstract":"<p>Let <span>(Gamma )</span> be a discrete subgroup of <span>(text {PU}(1,n))</span>. In this work, we look at the induced action of <span>(Gamma )</span> on the projective space <span>(mathbb {P}(wedge ^{k+1}mathbb {C}^{n+1}))</span> by the Plücker embedding, where <span>(wedge ^{k+1})</span> denotes the exterior power. We define a limit set for this action called the <i>k</i>-Chen-Greenberg limit set, which extends the classical definition of the Chen-Greenberg limit set <span>(L(Gamma ))</span>, and we show several of its properties. We prove that its Kulkarni limit set is the union taken over all <span>(pin L(Gamma ))</span> of the projective subspace generated by all <i>k</i>-planes that contain <i>p</i> or are contained in <span>(p^{perp })</span> via the Plücker embedding. We also prove a duality between both limit sets.</p>","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":"33 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508437","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":"Which Schubert Varieties are Hessenberg Varieties?","authors":"Laura Escobar, Martha Precup, John Shareshian","doi":"10.1007/s00031-023-09825-0","DOIUrl":"https://doi.org/10.1007/s00031-023-09825-0","url":null,"abstract":"<p>After proving that every Schubert variety in the full flag variety of a complex reductive group <i>G</i> is a general Hessenberg variety, we show that not all such Schubert varieties are adjoint Hessenberg varieties. In fact, in types A and C, we provide pattern avoidance criteria implying that the proportion of Schubert varieties that are adjoint Hessenberg varieties approaches zero as the rank of <i>G</i> increases. We show also that in type A, some Schubert varieties are not isomorphic to any adjoint Hessenberg variety.</p>","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":"61 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508439","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":"On the Invariant and Anti-Invariant Cohomologies of Hypercomplex Manifolds","authors":"Mehdi Lejmi, Nicoletta Tardini","doi":"10.1007/s00031-023-09828-x","DOIUrl":"https://doi.org/10.1007/s00031-023-09828-x","url":null,"abstract":"<p>A hypercomplex structure (<i>I</i>, <i>J</i>, <i>K</i>) on a manifold <i>M</i> is said to be <span>(C^infty )</span>-pure-and-full if the Dolbeault cohomology <span>(H^{2,0}_{partial }(M,I))</span> is the direct sum of two natural subgroups called the <span>(overline{J})</span>-invariant and the <span>(overline{J})</span>-anti-invariant subgroups. We prove that a compact hypercomplex manifold that satisfies the quaternionic version of the <span>(dd^c)</span>-Lemma is <span>(C^infty )</span>-pure-and-full. Moreover, we study the dimensions of the <span>(overline{J})</span>-invariant and the <span>(overline{J})</span>-anti-invariant subgroups, together with their analogue in the Bott-Chern cohomology. For instance, in real dimension 8, we characterize the existence of hyperkähler with torsion metrics in terms of the dimension of the <span>(overline{J})</span>-invariant subgroup. We also study the existence of special hypercomplex structures on almost abelian solvmanifolds.</p>","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":"62 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508438","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":"ON THE BRUHAT $$ mathcal{G} $$-ORDER BETWEEN LOCAL SYSTEMS ON THE B-ORBITS IN A HERMITIAN SYMMETRIC VARIETY","authors":"Michele Carmassi","doi":"10.1007/s00031-023-09824-1","DOIUrl":"https://doi.org/10.1007/s00031-023-09824-1","url":null,"abstract":"","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135959830","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":"A Moment Map for Twisted-Hamiltonian Vector Fields on Locally Conformally Kähler Manifolds","authors":"Daniele Angella, Simone Calamai, Francesco Pediconi, Cristiano Spotti","doi":"10.1007/s00031-023-09815-2","DOIUrl":"https://doi.org/10.1007/s00031-023-09815-2","url":null,"abstract":"Abstract We extend the classical Donaldson-Fujiki interpretation of the scalar curvature as moment map in Kähler geometry to the wider framework of locally conformally Kähler geometry.","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136263206","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":"Centralizers of Nilpotent Elements in Basic Classical Lie Superalgebras in Good Characteristic","authors":"Leyu Han","doi":"10.1007/s00031-023-09814-3","DOIUrl":"https://doi.org/10.1007/s00031-023-09814-3","url":null,"abstract":"Abstract Let $$mathfrak {g}=mathfrak {g}_{bar{0}}oplus mathfrak {g}_{bar{1}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;mml:mover&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;¯&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:mover&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;⊕&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;mml:mover&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;¯&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:mover&gt; &lt;/mml:msub&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; be a basic classical Lie superalgebra over an algebraically closed field $$mathbb {K}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;K&lt;/mml:mi&gt; &lt;/mml:math&gt; whose characteristic $$p&gt;0$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; is a good prime for $$mathfrak {g}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;/mml:math&gt; . Let $$G_{bar{0}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mover&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;¯&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:mover&gt; &lt;/mml:msub&gt; &lt;/mml:math&gt; be the reductive algebraic group over $$mathbb {K}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;K&lt;/mml:mi&gt; &lt;/mml:math&gt; such that $$textrm{Lie}(G_{bar{0}})=mathfrak {g}_{bar{0}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mtext&gt;Lie&lt;/mml:mtext&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mover&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;¯&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:mover&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;mml:mover&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;¯&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:mover&gt; &lt;/mml:msub&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; . Suppose $$ein mathfrak {g}_{bar{0}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;e&lt;/mml:mi&gt; &lt;mml:mo&gt;∈&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;mml:mover&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;¯&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:mover&gt; &lt;/mml:msub&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; is nilpotent. Write $$mathfrak {g}^{e}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;e&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;/mml:math&gt; for the centralizer of e in $$mathfrak {g}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;/mml:math&gt; and $$mathfrak {z}(mathfrak {g}^{e})$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;z&lt;/mml:mi&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;e&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; for the centre of $$mathfrak {g}^{e}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:msup&gt; &lt;mm","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135826708","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":"Compactifications of Moduli of G-Bundles and Conformal Blocks","authors":"Avery Wilson","doi":"10.1007/s00031-023-09820-5","DOIUrl":"https://doi.org/10.1007/s00031-023-09820-5","url":null,"abstract":"","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136108416","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":"Components of $$V(rho ) otimes V(rho )$$ and Dominant Weight Polyhedra for Affine Kac–Moody Lie Algebras","authors":"Sam Jeralds, Shrawan Kumar","doi":"10.1007/s00031-023-09823-2","DOIUrl":"https://doi.org/10.1007/s00031-023-09823-2","url":null,"abstract":"","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49611899","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":"LATTICE VERTEX ALGEBRAS AND LOOP GRASSMANNIANS","authors":"I. Mirkovic","doi":"10.1007/s00031-023-09821-4","DOIUrl":"https://doi.org/10.1007/s00031-023-09821-4","url":null,"abstract":"","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":"28 1","pages":"1221 - 1243"},"PeriodicalIF":0.7,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45797084","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}