scholarly journals Degenerate Flag Varieties of Type A and C are Schubert Varieties

2014 ◽  
Vol 2015 (15) ◽  
pp. 6353-6374 ◽  
Author(s):  
Giovanni Cerulli Irelli ◽  
Martina Lanini
Keyword(s):  
Type A ◽  
Schubert Varieties ◽  
Flag Varieties ◽  
Degenerate Flag 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

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 Semi-infinite Plücker Relations and Weyl Modules

2018 ◽  
Vol 2020 (14) ◽  
pp. 4357-4394 ◽  
Author(s):  
Evgeny Feigin ◽  
Ievgen Makedonskyi
Keyword(s):  
Type A ◽  
Character Formula ◽  
Flag Varieties ◽  
Coordinate Ring ◽  
Weyl Modules ◽  
Plücker Relations ◽  
Plücker Embedding ◽  
Formal Version ◽  
The Ideal

Abstract The goal of this paper is two-fold. First, we write down the semi-infinite Plücker relations, describing the Drinfeld–Plücker embedding of the (formal version of) semi-infinite flag varieties in type A. Second, we study the homogeneous coordinate ring, that is, the quotient by the ideal generated by the semi-infinite Plücker relations. We establish the isomorphism with the algebra of dual global Weyl modules and derive a new character formula.

scholarly journals DEGENERATE SCHUBERT VARIETIES IN TYPE A

2020 ◽  
Author(s):  
ROCCO CHIRIVÌ ◽  
XIN FANG ◽  
GHISLAIN FOURIER
Keyword(s):  
Type A ◽  
Schubert Varieties

scholarly journals K-Theoretic J-Functions of Type A Flag Varieties

2012 ◽  
Vol 2013 (16) ◽  
pp. 3647-3677
Author(s):  
K. Taipale
Keyword(s):  
Type A ◽  
Flag Varieties

scholarly journals Degenerate flag varieties in network coding

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ghislain Fourier ◽  
Gabriele Nebe
Keyword(s):  
Network Coding ◽  
Affine Space ◽  
Linear Subspace ◽  
Flag Varieties ◽  
Triangular Matrices ◽  
Upper Triangular Matrices ◽  
Rank Metric ◽  
Rank Metric Codes ◽  
Information Set ◽  
Degenerate Flag Varieties

<p style='text-indent:20px;'>Building upon the application of flags to network coding introduced in [<xref ref-type="bibr" rid="b6">6</xref>], we develop a variant of this coding technique that uses degenerate flags. The information set is a metric affine space isometric to the space of upper triangular matrices endowed with the flag rank metric. This suggests the development of a theory for flag rank metric codes in analogy to the rank metric codes used in linear subspace coding.</p>

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