Lecture 20. Families of affine Grassmannians

2020 ◽  
pp. 182-190
Keyword(s):  
Affine Grassmannians

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 On quiver varieties and affine Grassmannians of type A

2003 ◽  
Vol 336 (3) ◽  
pp. 207-212 ◽  
Author(s):  
Ivan Mirković ◽  
Maxim Vybornov
Keyword(s):  
Type A ◽  
Quiver Varieties ◽  
Affine Grassmannians

On a construction of affine Grassmannians and spine spaces

2001 ◽  
Vol 72 (1-2) ◽  
pp. 172-187 ◽  
Author(s):  
Krzysztof Prażmowski
Keyword(s):  
Affine Grassmannians

scholarly journals Smoothness of Schubert varieties in twisted affine Grassmannians

2020 ◽  
Vol 169 (17) ◽  
pp. 3223-3260
Author(s):  
Thomas J. Haines ◽  
Timo Richarz
Keyword(s):  
Schubert Varieties ◽  
Affine Grassmannians

scholarly journals The minimal degeneration singularities in the affine Grassmannians

2005 ◽  
Vol 126 (2) ◽  
pp. 233-249 ◽  
Author(s):  
Anton Malkin ◽  
Viktor Ostrik ◽  
Maxim Vybornov
Keyword(s):  
Affine Grassmannians

scholarly journals Degenerate affine Grassmannians and loop quivers

2017 ◽  
Vol 57 (2) ◽  
pp. 445-474
Author(s):  
Evgeny Feigin ◽  
Michael Finkelberg ◽  
Markus Reineke
Keyword(s):  
Affine Grassmannians

scholarly journals The ABC's of affine Grassmannians and Hall-Littlewood polynomials

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Avinash J. Dalal ◽  
Jennifer Morse
Keyword(s):  
Schur Functions ◽  
Type A ◽  
Combinatorial Formula ◽  
Transition Matrices ◽  
Nous Obtenons ◽  
Affine Grassmannians ◽  
Littlewood Polynomials ◽  
International Audience ◽  
Schubert Classes ◽  
Affine Type

International audience We give a new description of the Pieri rule for $k$-Schur functions using the Bruhat order on the affine type-$A$ Weyl group. In doing so, we prove a new combinatorial formula for representatives of the Schubert classes for the cohomology of affine Grassmannians. We show how new combinatorics involved in our formulas gives the Kostka-Foulkes polynomials and discuss how this can be applied to study the transition matrices between Hall-Littlewood and $k$-Schur functions. Nous présentons une nouvelle description, issue de l'ordre de Bruhat du groupe de Weyl affine de type $A$, de la règle de Pieri pour les fonctions $k$-Schur. Ce faisant, nous obtenons une nouvelle formule combinatoire pour les représentants des classes de Schubert de la cohomologie des Grassmannienne affines. Nous décrivons aussi comment notre approche permet d'obtenir les polynômes de Kostka-Foulkes et comment elle peut être appliquée à l’étude des matrices de transition entre les polynômes de Hall-Littlewood et les fonctions $k$-Schur.

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