Transformation Groups最新文献

{"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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 $$mathfrak {g}=mathfrak {g}_{bar{0}}oplus mathfrak {g}_{bar{1}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mover> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> <mml:mo>⊕</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mover> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> </mml:mrow> </mml:math> be a basic classical Lie superalgebra over an algebraically closed field $$mathbb {K}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>K</mml:mi> </mml:math> whose characteristic $$p&gt;0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> is a good prime for $$mathfrak {g}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>g</mml:mi> </mml:math> . Let $$G_{bar{0}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>G</mml:mi> <mml:mover> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> </mml:math> be the reductive algebraic group over $$mathbb {K}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>K</mml:mi> </mml:math> such that $$textrm{Lie}(G_{bar{0}})=mathfrak {g}_{bar{0}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mtext>Lie</mml:mtext> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>G</mml:mi> <mml:mover> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mover> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> </mml:mrow> </mml:math> . Suppose $$ein mathfrak {g}_{bar{0}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>e</mml:mi> <mml:mo>∈</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mover> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> </mml:mrow> </mml:math> is nilpotent. Write $$mathfrak {g}^{e}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mi>e</mml:mi> </mml:msup> </mml:math> for the centralizer of e in $$mathfrak {g}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>g</mml:mi> </mml:math> and $$mathfrak {z}(mathfrak {g}^{e})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mi>e</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> for the centre of $$mathfrak {g}^{e}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mm","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}

{"title":"A First Fundamental Theorem of Invariant Theory for the Quantum Queer Superalgebra","authors":"Z. Chang, Yongjie Wang","doi":"10.1007/s00031-023-09818-z","DOIUrl":"https://doi.org/10.1007/s00031-023-09818-z","url":null,"abstract":"","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44515564","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":"Quasi-Integrable Modules over Twisted Affine Lie Superalgebras","authors":"M. Yousofzadeh","doi":"10.1007/s00031-023-09805-4","DOIUrl":"https://doi.org/10.1007/s00031-023-09805-4","url":null,"abstract":"","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49613646","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}