Electrospun polyfunctional conductive anisotropic Janus-shaped film, derivative 3D Janus tube and 3D plus 2D complete flag-shaped structures

2020 ◽  
Vol 8 (19) ◽  
pp. 6565-6576
Author(s):  
Haina Qi ◽  
Qianli Ma ◽  
Yunrui Xie ◽  
Yan Song ◽  
Jiao Tian ◽  
...  
Keyword(s):  
Complete Flag

Anisotropic conductive–magnetic–luminescent 2D di-layer Janus-shaped film, derivative 3D Janus tube and 3D plus 2D complete flag-shaped structures are constructed.

scholarly journals Twisted gamma filtration and algebras with orthogonal involution

2014 ◽  
Vol 12 (3) ◽  
Author(s):  
Caroline Junkins
Keyword(s):  
Algebraic Group ◽  
Grothendieck Group ◽  
Linear Algebraic Group ◽  
Flag Variety ◽  
Flag Varieties ◽  
Torsion Element ◽  
Complete Flag ◽  
Gamma Filtration

AbstractFor the Grothendieck group of a split simple linear algebraic group, the twisted γ-filtration provides a useful tool for constructing torsion elements in -rings of twisted flag varieties. In this paper, we construct a non-trivial torsion element in the γ-ring of a complete flag variety twisted by means of a PGO-torsor. This generalizes the construction in the HSpin case previously obtained by Zainoulline.

scholarly journals FROM COMPLETE TO PARTIAL FLAGS IN GEOMETRIC EXTENSION ALGEBRAS

2017 ◽  
Vol 60 (1) ◽  
pp. 111-121
Author(s):  
JULIA SAUTER
Keyword(s):  
Vector Bundles ◽  
Homogeneous Spaces ◽  
Locally Finite ◽  
Perverse Sheaf ◽  
Constant Sheaf ◽  
Push Forward ◽  
Complete Flag ◽  
Extension Algebra ◽  
The Relationship ◽  
Homogeneous Vector

AbstractA geometric extension algebra is an extension algebra of a semi-simple perverse sheaf (allowing shifts), e.g., a push-forward of the constant sheaf under a projective map. Particular nice situations arise for collapsings of homogeneous vector bundles over homogeneous spaces. In this paper, we study the relationship between partial flag and complete flag cases. Our main result is that the locally finite modules over the geometric extension algebras are related by a recollement. As examples, we investigate parabolic affine nil Hecke algebras, geometric extension algebras associated with parabolic Springer maps and an example of Reineke of a parabolic quiver-graded Hecke algebra.

scholarly journals 0-Hecke algebra actions on coinvariants and flags

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Jia Huang
Keyword(s):  
Generating Functions ◽  
Hecke Algebra ◽  
Flag Variety ◽  
Major Index ◽  
Inversion Number ◽  
International Audience ◽  
Descent Set ◽  
Complete Flag ◽  
Coinvariant Algebra

International audience By investigating the action of the 0-Hecke algebra on the coinvariant algebra and the complete flag variety, we interpret generating functions counting the permutations with fixed inverse descent set by their inversion number and major index. En étudiant l'action de l'algèbre de 0-Hecke sur l'algèbre coinvariante et la variété de drapeaux complète, nous interprétons les fonctions génératrices qui comptent les permutations avec un ensemble inverse de descentes fixé, selon leur nombre d'inversions et leur "major index''.

scholarly journals Cycle-Level Intersection Theory for Toric Varieties

2004 ◽  
Vol 56 (5) ◽  
pp. 1094-1120
Author(s):  
Hugh Thomas
Keyword(s):  
Toric Variety ◽  
Linear Subspace ◽  
Toric Varieties ◽  
Cartier Divisor ◽  
Ring Structure ◽  
Intersection Theory ◽  
Inner Product ◽  
Characteristic Classes ◽  
Level Intersection ◽  
Complete Flag

AbstractThis paper addresses the problem of constructing a cycle-level intersection theory for toric varieties. We show that by making one global choice, we can determine a cycle representative for the intersection of an equivariant Cartier divisor with an invariant cycle on a toric variety. For a toric variety defined by a fan inN, the choice consists of giving an inner product or a complete flag forMQ= ℚ ⊗ Hom(N, ℤ), or more generally giving for each cone σ in the fan a linear subspace ofMQcomplementary to σ⊥, satisfying certain compatibility conditions. We show that these intersection cycles have properties analogous to the usual intersections modulo rational equivalence. IfXis simplicial (for instance, ifXis non-singular), we obtain a commutative ring structure to the invariant cycles ofXwith rational coefficients. This ring structure determines cycles representing certain characteristic classes of the toric variety. We also discuss how to define intersection cycles that require no choices, at the expense of increasing the size of the coefficient field.

scholarly journals Flag Gromov-Witten invariants via crystals

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Jennifer Morse ◽  
Anne Schilling
Keyword(s):  
Weyl Group ◽  
Type A ◽  
Schubert Calculus ◽  
Schur Function ◽  
Flag Varieties ◽  
Highest Weight ◽  
Affine Weyl Group ◽  
Nous Montrons ◽  
International Audience ◽  
Complete Flag

International audience We apply ideas from crystal theory to affine Schubert calculus and flag Gromov-Witten invariants. By defining operators on certain decompositions of elements in the type-$A$ affine Weyl group, we produce a crystal reflecting the internal structure of Specht modules associated to permutation diagrams. We show how this crystal framework can be applied to study the product of a Schur function with a $k$-Schur function. Consequently, we prove that a subclass of 3-point Gromov-Witten invariants of complete flag varieties for $\mathbb{C}^n$ enumerate the highest weight elements under these operators. Nous appliquons des idées provenant de la théorie des bases cristallines au calcul de Schubert affine et aux invariants de drapeaux de Gromov–Witten. Nous définissons des opérateurs sur certaines décompositions d’éléments de groupes de Weyl affines en type $A$ afin de construire une base cristalline encodant la structure interne des modules de Specht associés aux diagrammes de permutations. Nous montrons comment la structure de cristal permet d’étudier le produit d’une fonction de Schur avec une $k$-fonction de Schur. En conséquence, nous prouvons que la sous-classe des invariants de 3-points de Gromov–Witten d’une variété complète de drapeaux complets pour $\mathbb{C}^n$ énumère les éléments de poids maximaux pour ces opérateurs.

scholarly journals A Divided Difference Operator

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Nicholas Teff
Keyword(s):  
Difference Operator ◽  
Divided Difference ◽  
Root Systems ◽  
Bruhat Order ◽  
Flag Variety ◽  
International Audience ◽  
Complete Flag ◽  
Special Case

International audience We construct a divided difference operator using GKM theory. This generalizes the classical divided difference operator for the cohomology of the complete flag variety. This construction proves a special case of a recent conjecture of Shareshian and Wachs. Our methods are entirely combinatorial and algebraic, and rely heavily on the combinatorics of root systems and Bruhat order.

scholarly journals Manifolds of Isospectral Matrices and Hessenberg Varieties

2020 ◽  
Author(s):  
Anton Ayzenberg ◽  
Victor Buchstaber
Keyword(s):  
Smooth Manifold ◽  
Flag Variety ◽  
Natural Action ◽  
Cohomology Rings ◽  
Compact Torus ◽  
Hessenberg Varieties ◽  
Toda Flow ◽  
Odd Degree ◽  
Complete Flag ◽  
The Given

Abstract We consider the space $X_h$ of Hermitian matrices having staircase form and the given simple spectrum. There is a natural action of a compact torus on this space. Using generalized Toda flow, we show that $X_h$ is a smooth manifold and its smooth type is independent of the spectrum. Morse theory is then used to show the vanishing of odd degree cohomology, so that $X_h$ is an equivariantly formal manifold. The equivariant and ordinary cohomology rings of $X_h$ are described using GKM theory. The main goal of this paper is to show the connection between the manifolds $X_h$ and regular semisimple Hessenberg varieties well known in algebraic geometry. Both spaces $X_h$ and Hessenberg varieties form wonderful families of submanifolds in the complete flag variety. There is a certain symmetry between these families, which can be generalized to other submanifolds of the flag variety.

ON GRÖBNER BASES FOR FLAG MANIFOLDS F(1, 1, … , 1, n)

2012 ◽  
Vol 12 (03) ◽  
pp. 1250182
Author(s):  
ZORAN Z. PETROVIĆ ◽  
BRANISLAV I. PRVULOVIĆ
Keyword(s):  
Vector Fields ◽  
Polynomial Algebra ◽  
Gröbner Bases ◽  
Flag Manifold ◽  
Grobner Bases ◽  
Flag Manifolds ◽  
Embedding Dimension ◽  
The Real ◽  
Real Flag Manifold ◽  
Complete Flag

The knowledge of cohomology of a manifold has shown to be quite relevant in various investigations: the question of vector fields, immersion and embedding dimension, and recently even in topological robotics. The method of Gröbner bases is applicable when the cohomology of the manifold is a quotient of a polynomial algebra. The mod 2 cohomology of the real flag manifold F(n1, n2, …, nr) is known to be isomorphic to a polynomial algebra modulo a certain ideal. Reduced Gröbner bases for these ideals are obtained in the case of manifolds F(1, 1, …, 1, n) including the complete flag manifolds (n = 1).

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