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 test function conjecture for local models of Weil-restricted groups

2020 ◽  
Vol 156 (7) ◽  
pp. 1348-1404
Author(s):  
Thomas J. Haines ◽  
Timo Richarz
Keyword(s):  
Level Structure ◽  
Local Fields ◽  
Shimura Varieties ◽  
Reductive Groups ◽  
Loop Groups ◽  
Local Models ◽  
Test Function ◽  
Affine Grassmannians ◽  
Affine Scheme ◽  
Relative Curve

We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure attached to Weil-restricted groups, as defined by B. Levin. Our result covers the (modified) local models attached to all connected reductive groups over $p$-adic local fields with $p\geqslant 5$. In addition, we give a self-contained study of relative affine Grassmannians and loop groups formed using general relative effective Cartier divisors in a relative curve over an arbitrary Noetherian affine scheme.

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
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