scholarly journals A COMBINATORIAL STUDY OF AFFINE SCHUBERT VARIETIES IN THE AFFINE GRASSMANNIAN

2021 ◽  
Author(s):  
MARC BESSON ◽  
JIUZU HONG
Keyword(s):  
Schubert Varieties ◽  
Affine Grassmannian

scholarly journals ON A REDUCEDNESS CONJECTURE FOR SPHERICAL SCHUBERT VARIETIES AND SLICES IN THE AFFINE GRASSMANNIAN

2017 ◽  
Vol 23 (3) ◽  
pp. 707-722 ◽  
Author(s):  
JOEL KAMNITZER ◽  
DINAKAR MUTHIAH ◽  
ALEX WEEKES
Keyword(s):  
Schubert Varieties ◽  
Affine Grassmannian

The BdR+-affine Grassmannian

2020 ◽  
pp. 169-181
Author(s):  
Peter Scholze ◽  
Jared Weinstein
Keyword(s):  
Schubert Variety ◽  
Reductive Group ◽  
Schubert Varieties ◽  
Affine Grassmannian ◽  
Singular Varieties

This chapter defines an object that was one of the big motivations to develop a theory of diamonds. In the study of the usual Grassmannian variety G/B attached to a reductive group G, one defines a Schubert variety to be the closure of a B-orbit in G/B. Generally, Schubert varieties are singular varieties. Desingularizations of Schubert varieties are constructed by Demazure. The chapter uses an analogue of this construction in the context of the B+ dR-Grassmannian. It then looks at miniscule Schubert varieties. In this case, one can identify the space explicitly. If µ is minuscule, the Bialynicki–Birula map is an isomorphism.

scholarly journals Polynomial identities related to special Schubert varieties

2021 ◽  
Author(s):  
Francesca Cioffi ◽  
Davide Franco ◽  
Carmine Sessa
Keyword(s):  
Arbitrary Number ◽  
Schubert Variety ◽  
Decomposition Theorem ◽  
Point Of View ◽  
Explicit Description ◽  
Intersection Cohomology ◽  
Schubert Varieties ◽  
Polynomial Identities ◽  
Poincaré Polynomial

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

scholarly journals On a conjecture of Pappas and Rapoport about the standard local model for GL_d

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinakar Muthiah ◽  
Alex Weekes ◽  
Oded Yacobi
Keyword(s):  
Type A ◽  
Positive Answer ◽  
Local Model ◽  
Schubert Varieties ◽  
Shimura Varieties ◽  
Local Models ◽  
Full Generality ◽  
Frobenius Splitting ◽  
Affine Grassmannians ◽  
Main Ideas

AbstractIn their study of local models of Shimura varieties for totally ramified extensions, Pappas and Rapoport posed a conjecture about the reducedness of a certain subscheme of {n\times n} matrices. We give a positive answer to their conjecture in full generality. Our main ideas follow naturally from two of our previous works. The first is our proof of a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman on the equations defining type A affine Grassmannians. The second is the work of the first two authors and Kamnitzer on affine Grassmannian slices and their reduced scheme structure. We also present a version of our argument that is almost completely elementary: the only non-elementary ingredient is the Frobenius splitting of Schubert varieties.

On Schubert varieties in the flag manifold of Sl(n,?)

1987 ◽  
Vol 276 (2) ◽  
pp. 205-224 ◽  
Author(s):  
Kevin M. Ryan
Keyword(s):  
Flag Manifold ◽  
Schubert Varieties

scholarly journals A Mathematica Program for the Degrees of Certain Schubert Varieties

2002 ◽  
Vol 33 (4) ◽  
pp. 507-517 ◽  
Author(s):  
Xu an Zhao ◽  
Haibao Duan
Keyword(s):  
Schubert Varieties

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.

scholarly journals Torus Quotients of Schubert Varieties

2020 ◽  
Author(s):  
B. Narasimha Chary ◽  
S. K. Pattanayak
Keyword(s):  
Schubert Varieties
Sign in / Sign up

Export Citation Format

Share Document