The fixed point subvarieties of unipotent transformations on generalized flag varieties and the green functions

1979 ◽  
Vol 241 (3) ◽  
pp. 193-208 ◽  
Author(s):  
R. Hotta ◽  
N. Shimomura
Keyword(s):  
Fixed Point ◽  
Green Functions ◽  
Flag Varieties

scholarly journals A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY

2019 ◽  
Vol 7 ◽  
Author(s):  
ARAM BINGHAM ◽  
MAHIR BILEN CAN ◽  
YILDIRAY OZAN
Keyword(s):  
Fixed Point ◽  
Maximal Torus ◽  
Flag Varieties ◽  
Direct Sum ◽  
Equivariant Embedding ◽  
Graded Module ◽  
Homogeneous Variety

Let $G/H$ be a homogeneous variety and let $X$ be a $G$ -equivariant embedding of $G/H$ such that the number of $G$ -orbits in $X$ is finite. We show that the equivariant Borel–Moore homology of $X$ has a filtration with associated graded module the direct sum of the equivariant Borel–Moore homologies of the $G$ -orbits. If $T$ is a maximal torus of $G$ such that each $G$ -orbit has a $T$ -fixed point, then the equivariant filtration descends to give a filtration on the ordinary Borel–Moore homology of $X$ . We apply our findings to certain wonderful compactifications as well as to double flag varieties.

On Orbit Closures of Symmetric Subgroups in Flag Varieties

2000 ◽  
Vol 52 (2) ◽  
pp. 265-292 ◽  
Author(s):  
Michel Brion ◽  
Aloysius G. Helminck
Keyword(s):  
Fixed Point ◽  
Borel Subgroup ◽  
Reductive Group ◽  
Double Coset ◽  
Restriction Map ◽  
Flag Varieties ◽  
Parabolic Subgroups ◽  
Involutive Automorphism ◽  
Orbit Closures ◽  
Geometric Analogue

AbstractWe study K-orbits in G/P where G is a complex connected reductive group, P ⊆ G is a parabolic subgroup, and K ⊆ G is the fixed point subgroup of an involutive automorphism θ. Generalizing work of Springer, we parametrize the (finite) orbit set K \ G/P and we determine the isotropy groups. As a consequence, we describe the closed (resp. affine) orbits in terms of θ-stable (resp. θ-split) parabolic subgroups. We also describe the decomposition of any (K, P)-double coset in G into (K, B)-double cosets, where B ⊆ P is a Borel subgroup. Finally, for certain K-orbit closures X ⊆ G/B, and for any homogeneous line bundle on G/B having nonzero global sections, we show that the restriction map resX : H0(G/B, ) → H0(X, ) is surjective and that Hi(X, ) = 0 for i ≥ 1. Moreover, we describe the K-module H0(X, ). This gives information on the restriction to K of the simple G-module H0(G/B, ). Our construction is a geometric analogue of Vogan and Sepanski’s approach to extremal K-types.

scholarly journals On the existence of positive solutions for generalized fractional boundary value problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Arjumand Seemab ◽  
Mujeeb Ur Rehman ◽  
Jehad Alzabut ◽  
Abdelouahed Hamdi
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Green Functions ◽  
Fractional Operators ◽  
Existence Of Positive Solutions ◽  
Different Types ◽  
Fractional Boundary Value Problems

AbstractThe existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of fixed point theorems. For the sake of converting the proposed problems into integral equations, we construct Green functions and study their properties for three different types of boundary value problems. Examples are presented to demonstrate the validity of theoretical findings.

scholarly journals Goresky–MacPherson Calculus for the Affine Flag Varieties

2010 ◽  
Vol 62 (2) ◽  
pp. 473-480 ◽  
Author(s):  
Zhiwei Yun
Keyword(s):  
Fixed Point ◽  
Equivariant Cohomology ◽  
Flag Variety ◽  
Moment Map ◽  
Flag Varieties ◽  
The Moment ◽  
Affine Flag Variety ◽  
Affine Flag

AbstractWe use the fixed point arrangement technique developed by Goresky and MacPherson to calculate the part of the equivariant cohomology of the affine flag variety ℱ ℓ G generated by degree 2. We use this result to show that the vertices of the moment map image of ℱ ℓ G lie on a paraboloid.

scholarly journals Quasi-split symmetric pairs of 𝑈(𝔰𝔩_{𝔫}) and Steinberg varieties of classical type

2021 ◽  
Vol 25 (32) ◽  
pp. 903-934
Author(s):  
Yiqiang Li
Keyword(s):  
Fixed Point ◽  
Geometric Realization ◽  
Classical Type ◽  
Symmetric Pair ◽  
Flag Varieties ◽  
Projective System ◽  
Content Type ◽  
Lagrangian Construction

We provide a Lagrangian construction for the fixed-point subalgebra, together with its idempotent form, in a quasi-split symmetric pair of type A n − 1 A_{n-1} . This is obtained inside the limit of a projective system of Borel-Moore homologies of the Steinberg varieties of n n -step isotropic flag varieties. Arising from the construction are a basis of homological origin for the idempotent form and a geometric realization of rational modules.

Mental equilibrium: Identifying fixed-point attractors in the stream of thought

2003 ◽  
Author(s):  
Robin R. Vallacher ◽  
Andrzej Nowak ◽  
Matthew Rockloff
Keyword(s):  
Fixed Point
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