scholarly journals Schubert varieties in twisted affine flag varieties and local models

2013 ◽  
Vol 375 ◽  
pp. 121-147 ◽  
Author(s):  
Timo Richarz
Keyword(s):  
Schubert Varieties ◽  
Flag Varieties ◽  
Local Models ◽  
Affine Flag

scholarly journals Local models in the ramified case. III Unitary groups

2009 ◽  
Vol 8 (3) ◽  
pp. 507-564 ◽  
Author(s):  
G. Pappas ◽  
M. Rapoport
Keyword(s):  
Local Structure ◽  
Level Structure ◽  
Quadratic Extension ◽  
Unitary Groups ◽  
Shimura Varieties ◽  
Flag Varieties ◽  
Shimura Variety ◽  
Local Models ◽  
Affine Flag

AbstractWe continue our study of the reduction of PEL Shimura varieties with parahoric level structure at primespat which the group defining the Shimura variety ramifies. We describe ‘good’p-adic integral models of these Shimura varieties and study their étale local structure. In the present paper we mainly concentrate on the case of unitary groups for a ramified quadratic extension. Some of our results are applications of the theory of twisted affine flag varieties that we developed in a previous paper.

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.

scholarly journals Degenerate flag varieties and Schubert varieties: a characteristic free approach

2016 ◽  
Vol 284 (2) ◽  
pp. 283-308 ◽  
Author(s):  
Giovanni Cerulli Irelli ◽  
Martina Lanini ◽  
Peter Littelmann
Keyword(s):  
Schubert Varieties ◽  
Flag Varieties ◽  
Degenerate Flag Varieties

Affine flag varieties

2020 ◽  
pp. 191-206
Author(s):  
Peter Scholze ◽  
Jared Weinstein
Keyword(s):  
Group Scheme ◽  
Flag Variety ◽  
Flag Varieties ◽  
Connected Component ◽  
Witt Vector ◽  
Classical Definition ◽  
Definition Of ◽  
Affine Flag Variety ◽  
Affine Flag

This chapter reviews affine flag varieties. It generalizes some of the previous results to the case where G over Zp is a parahoric group scheme. In fact, slightly more generally, it allows the case that the special fiber is not connected, with connected component of the identity G? being a parahoric group scheme. This case comes up naturally in the classical definition of Rapoport-Zink spaces. The chapter first discusses the Witt vector affine flag variety over Fp. This is an increasing union of perfections of quasiprojective varieties along closed immersions. In the case that G° is parahoric, one gets ind-properness.

scholarly journals Twisted loop groups and their affine flag varieties

2008 ◽  
Vol 219 (1) ◽  
pp. 118-198 ◽  
Author(s):  
G. Pappas ◽  
M. Rapoport
Keyword(s):  
Flag Varieties ◽  
Loop Groups ◽  
Affine Flag

scholarly journals Degenerate Affine Flag Varieties and Quiver Grassmannians

2020 ◽  
Author(s):  
Alexander Pütz
Keyword(s):  
Flag Varieties ◽  
Rational Singularities ◽  
Quiver Grassmannians ◽  
Finite Dimensional ◽  
Irreducible Components ◽  
Affine Flag

AbstractWe study finite dimensional approximations to degenerate versions of affine flag varieties using quiver Grassmannians for cyclic quivers. We prove that they admit cellular decompositions parametrized by affine Dellac configurations, and that their irreducible components are normal Cohen-Macaulay varieties with rational singularities.

Euler characteristic of certain affine flag varieties

1996 ◽  
Vol 1 (1-2) ◽  
pp. 35-39 ◽  
Author(s):  
C. Kenneth Fan
Keyword(s):  
Euler Characteristic ◽  
Flag Varieties ◽  
Affine Flag

scholarly journals Total positivity for the Lagrangian Grassmannian

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Rachel Karpman
Keyword(s):  
Symplectic Form ◽  
Total Positivity ◽  
Combinatorial Structure ◽  
Schubert Varieties ◽  
Flag Varieties ◽  
Young Diagrams ◽  
Lagrangian Grassmannian ◽  
Planar Network ◽  
International Audience ◽  
Isotropic Subspaces

International audience The positroid decomposition of the Grassmannian refines the well-known Schubert decomposition, and has a rich combinatorial structure. There are a number of interesting combinatorial posets which index positroid varieties,just as Young diagrams index Schubert varieties. In addition, Postnikov’s boundary measurement map gives a family of parametrizations for each positroid variety. The domain of each parametrization is the space of edge weights of a weighted planar network. The positroid stratification of the Grassmannian provides an elementary example of Lusztig’s theory of total non negativity for partial flag varieties, and has remarkable applications to particle physics.We generalize the combinatorics of positroid varieties to the Lagrangian Grassmannian, the moduli space of maximal isotropic subspaces with respect to a symplectic form

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