Orbit-closure partitions

1955 ◽  
pp. 12-19
Keyword(s):  
Orbit Closure

scholarly journals Algorithms for orbit closure separation for invariants and semi-invariants of matrices

2020 ◽  
Vol 14 (10) ◽  
pp. 2791-2813
Author(s):  
Harm Derksen ◽  
Visu Makam
Keyword(s):  
Orbit Closure

scholarly journals Poincaré polynomials of generic torus orbit closures in Schubert varieties

2021 ◽  
pp. 189-208
Author(s):  
Eunjeong Lee ◽  
Mikiya Masuda ◽  
Seonjeong Park ◽  
Jongbaek Song
Keyword(s):  
Schubert Variety ◽  
Flag Variety ◽  
Schubert Varieties ◽  
Orbit Closure ◽  
Poincaré Polynomial ◽  
Content Type ◽  
Eulerian Polynomial ◽  
Orbit Closures

The closure of a generic torus orbit in the flag variety G / B G/B of type  A A is known to be a permutohedral variety, and its Poincaré polynomial agrees with the Eulerian polynomial. In this paper, we study the Poincaré polynomial of a generic torus orbit closure in a Schubert variety in  G / B G/B . When the generic torus orbit closure in a Schubert variety is smooth, its Poincaré polynomial is known to agree with a certain generalization of the Eulerian polynomial. We extend this result to an arbitrary generic torus orbit closure which is not necessarily smooth.

Generalized heredity in ℬ-free systems

2021 ◽  
pp. 2140008
Author(s):  
Gerhard Keller
Keyword(s):  
Orbit Closure ◽  
Light Tails ◽  
Free Sets

Let [Formula: see text] be a primitive set, [Formula: see text], [Formula: see text], and denote by [Formula: see text] the orbit closure of [Formula: see text] under the shift. We complement results on heredity of [Formula: see text] from [Dymek et al., [Formula: see text]-free sets and dynamics, Trans. Amer. Math. Soc. 370 (2018) 5425–5489] in two directions: In the proximal case we prove that a certain subshift [Formula: see text], which coincides with [Formula: see text] when [Formula: see text] is taut, is always hereditary. (In particular there is no need for the stronger assumption that the set [Formula: see text] has light tails, as in [Dymek et al., [Formula: see text]-free sets and dynamics, Trans. Amer. Math. Soc. 370 (2018) 5425–5489].) We also generalize the concept of heredity to include the non-proximal (and hence non-hereditary) case by proving that [Formula: see text] is always “hereditary above its unique minimal (Toeplitz) subsystem”. Finally, we characterize this Toeplitz subsystem as being a set [Formula: see text], where [Formula: see text] for a set [Formula: see text] that can be derived from [Formula: see text], and draw some further conclusions from this characterization. Throughout results from [Kasjan et al., Dynamics of [Formula: see text]-free sets: A view through the window, Int. Math. Res. Not. 2019 (2019) 2690–2734] are heavily used.

scholarly journals Unobstructed symplectic packing for tori and hyper-Kähler manifolds

2016 ◽  
Vol 08 (04) ◽  
pp. 589-626 ◽  
Author(s):  
Michael Entov ◽  
Misha Verbitsky
Keyword(s):  
Structure Theorem ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Orbit Closure ◽  
Kahler Manifolds ◽  
Dimensional Torus ◽  
Symplectic Forms ◽  
Kahler Manifold ◽  
Symplectic Packing ◽  
Smooth Deformation

Let [Formula: see text] be a closed symplectic manifold of volume [Formula: see text]. We say that the symplectic packings of [Formula: see text] by balls are unobstructed if any collection of disjoint symplectic balls (of possibly different radii) of total volume less than [Formula: see text] admits a symplectic embedding to [Formula: see text]. In 1994, McDuff and Polterovich proved that symplectic packings of Kähler manifolds by balls can be characterized in terms of the Kähler cones of their blow-ups. When [Formula: see text] is a Kähler manifold which is not a union of its proper subvarieties (such a manifold is called Campana simple), these Kähler cones can be described explicitly using the Demailly and Paun structure theorem. We prove that for any Campana simple Kähler manifold, as well as for any manifold which is a limit of Campana simple manifolds in a smooth deformation, the symplectic packings by balls are unobstructed. This is used to show that the symplectic packings by balls of all even-dimensional tori equipped with Kähler symplectic forms and of all hyper-Kähler manifolds of maximal holonomy are unobstructed. This generalizes a previous result by Latschev–McDuff–Schlenk. We also consider symplectic packings by other shapes and show, using Ratner’s orbit closure theorem, that any even-dimensional torus equipped with a Kähler form whose cohomology class is not proportional to a rational one admits a full symplectic packing by any number of equal polydisks (and, in particular, by any number of equal cubes).

scholarly journals JOSEPH IDEALS AND LISSE MINIMAL -ALGEBRAS

2016 ◽  
Vol 17 (2) ◽  
pp. 397-417 ◽  
Author(s):  
Tomoyuki Arakawa ◽  
Anne Moreau
Keyword(s):  
Nilpotent Orbit ◽  
Vertex Algebras ◽  
Orbit Closure ◽  
New Family ◽  
Orbit Closures

We consider a lifting of Joseph ideals for the minimal nilpotent orbit closure to the setting of affine Kac–Moody algebras and find new examples of affine vertex algebras whose associated varieties are minimal nilpotent orbit closures. As an application we obtain a new family of lisse ($C_{2}$-cofinite)$W$-algebras that are not coming from admissible representations of affine Kac–Moody algebras.

scholarly journals On minimal self-joinings in topological dynamics

1987 ◽  
Vol 7 (2) ◽  
pp. 211-227 ◽  
Author(s):  
Andrés del Junco
Keyword(s):  
Automorphism Group ◽  
Ergodic Theory ◽  
Metric Space ◽  
Topological Dynamics ◽  
Orbit Closure ◽  
Compact Metric Space ◽  
Minimal Self ◽  
Finite Set ◽  
Countably Infinite

AbstractIf X is a compact metric space and T a homeomorphism of X we say (X, T) has almost minimal power joinings (AMPJ) if there is a dense GδX* in X such that for each finite set k, x∈(X*)k and l:k → ℤ−{0}, the orbit closure cl {} is a product of off-diagonals (POOD) on Xk. By an offdiagonal on Xk′, k′k we mean a set of the form (⊗,j∈k′Tm(j))Δ, Δ the diagonal in Xk′, m:k′→ℤ any function, and by a POOD on Xk we mean that k is split into subsets k′, on each Xk′ we put an off-diagonal and then we take the product of these.We show that examples of AMPJ exist and that this definition leads to a theory completely analogous to Rudolph's theory of minimal self-joinings in ergodic theory. In particular if (X, T) has AMPJ the automorphism group of T is {Tn}, T has only almost 1-1 factors (other than the trivial one) and the automorphism group and factors of ⊕i ∊ kT, k finite or countably infinite, can be very explicitly described. We also discuss ℝ-actions.

scholarly journals A nonhomogeneous orbit closure of a diagonal subgroup

2010 ◽  
Vol 171 (1) ◽  
pp. 557-570 ◽  
Author(s):  
François Maucourant
Keyword(s):  
Orbit Closure ◽  
Diagonal Subgroup

scholarly journals The orbit of a Hölder continuous path under a hyperbolic toral automorphism

1983 ◽  
Vol 3 (3) ◽  
pp. 345-349 ◽  
Author(s):  
M. C. Irwin
Keyword(s):  
Orbit Closure ◽  
Continuous Path ◽  
Toral Automorphism ◽  
Hölder Continuous ◽  
Linear Automorphism ◽  
Hyperbolic Toral Automorphism

AbstractLet f:T3→T3 be a hyperbolic toral automorphism lifting to a linear automorphism with real eigenvalues. We prove that there is a Hölder continuous path in T3 whose orbit-closure is 1-dimensional. This strengthens results of Hancock and Przytycki concerning continuous paths, and contrasts with results of Franks and Mañé concerning rectifiable paths.

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