scholarly journals Modular perverse sheaves on flag varieties I: tilting and parity sheaves

2016 ◽  
Vol 49 (2) ◽  
pp. 325-370 ◽  
Author(s):  
N. Pramod Achar ◽  
Simon
Keyword(s):  
Flag Varieties ◽  
Perverse Sheaves

scholarly journals Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups

2019 ◽  
Vol 72 (1) ◽  
pp. 1-55
Author(s):  
Pramod N. Achar ◽  
Simon Riche ◽  
Cristian Vay
Keyword(s):  
Coxeter Group ◽  
Coxeter Groups ◽  
Grothendieck Group ◽  
General Setting ◽  
Hecke Algebra ◽  
Abelian Category ◽  
Flag Varieties ◽  
Perverse Sheaves

AbstractIn this paper we construct an abelian category of mixed perverse sheaves attached to any realization of a Coxeter group, in terms of the associated Elias–Williamson diagrammatic category. This construction extends previous work of the first two authors, where we worked with parity complexes instead of diagrams, and we extend most of the properties known in this case to the general setting. As an application we prove that the split Grothendieck group of the Elias–Williamson diagrammatic category is isomorphic to the corresponding Hecke algebra, for any choice of realization.

scholarly journals Nearby cycles of Whittaker sheaves on Drinfeld’s compactification

2018 ◽  
Vol 154 (8) ◽  
pp. 1775-1800
Author(s):  
Justin Campbell
Keyword(s):  
Lie Algebra ◽  
Geometric Construction ◽  
Intersection Cohomology ◽  
Flag Varieties ◽  
Perverse Sheaves ◽  
Nilpotent Radical ◽  
Perverse Sheaf ◽  
Nearby Cycles

In this article we give a geometric construction of a tilting perverse sheaf on Drinfeld’s compactification, by applying the nearby cycles functor to a family of nondegenerate Whittaker sheaves. Its restrictions along the defect stratification are shown to be certain perverse sheaves attached to the nilpotent radical of the Langlands dual Lie algebra. We also describe the subquotients of the monodromy filtration using the Picard–Lefschetz oscillators introduced by Schieder. We give an argument that the subquotients are semisimple based on the action, constructed by Feigin, Finkelberg, Kuznetsov, and Mirković, of the Langlands dual Lie algebra on the global intersection cohomology of quasimaps into flag varieties.

Tropical flag varieties

2021 ◽  
Vol 384 ◽  
pp. 107695
Author(s):  
Madeline Brandt ◽  
Christopher Eur ◽  
Leon Zhang
Keyword(s):  
Flag Varieties

scholarly journals Projective normality of torus quotients of flag varieties

2020 ◽  
Vol 224 (10) ◽  
pp. 106389
Author(s):  
Arpita Nayek ◽  
S.K. Pattanayak ◽  
Shivang Jindal
Keyword(s):  
Flag Varieties ◽  
Projective Normality

scholarly journals Euler characteristics in the quantum K-theory of flag varieties

2020 ◽  
Vol 26 (2) ◽  
Author(s):  
Anders S. Buch ◽  
Sjuvon Chung ◽  
Changzheng Li ◽  
Leonardo C. Mihalcea
Keyword(s):  
Flag Varieties ◽  
Euler Characteristics ◽  
K Theory

Explicit Models for Perverse Sheaves, II

2007 ◽  
Vol 11 (2) ◽  
pp. 149-178 ◽  
Author(s):  
F. Gudiel-Rodríguez ◽  
L. Narváez-Macarro
Keyword(s):  
Perverse Sheaves

Perverse sheaves on rank stratifications

1999 ◽  
Vol 96 (2) ◽  
pp. 317-362 ◽  
Author(s):  
Tom Braden ◽  
Mikhail Grinberg
Keyword(s):  
Perverse Sheaves

Chow groups of some generically twisted flag varieties

2017 ◽  
Vol 2 (2) ◽  
pp. 341-356 ◽  
Author(s):  
Nikita Karpenko
Keyword(s):  
Chow Groups ◽  
Flag Varieties
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