Corpus ID: 119644708

Following Schubert varieties under Feigin's degeneration of the flag variety

@article{Bossinger2018FollowingSV,
  title={Following Schubert varieties under Feigin's degeneration of the flag variety},
  author={Lara Bossinger and Martina Lanini},
  journal={arXiv: Representation Theory},
  year={2018}
}
We describe the effect of Feigin's flat degeneration of the type $\textrm{A}$ flag variety on its Schubert varieties. In particular, we study when they stay irreducible and in several cases we are able to encode reducibility of the degenerations in terms of symmetric group combinatorics. As a side result, we obtain an identification of some Schubert varieties with Richardson varieties in higher rank partial flag varieties. 
3 Citations

Figures and Tables from this paper

DEGENERATE SCHUBERT VARIETIES IN TYPE A
We introduce rectangular elements in the symmetric group. In the framework of PBW degenerations, we show that in type A the degenerate Schubert variety associated to a rectangular element is indeed aExpand
Standard monomial theory and toric degenerations of Richardson varieties inside Grassmannians and flag varieties
We study toric degenerations of opposite Schubert and Richardson varieties inside degenerations of Grassmannians and flag varieties. These degenerations are parametrized by matching fields in theExpand
Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian
Richardson varieties are obtained as intersections of Schubert and opposite Schubert varieties. We provide a new family of toric degenerations of Richardson varieties inside Grassmannians by studyingExpand

References

SHOWING 1-10 OF 15 REFERENCES
Toric degenerations of Schubert varieties
LetG be a simply connected semisimple complex algebraic group. We prove that every Schubert variety ofG has a flat degeneration into a toric variety. This provides a generalization of results of [9],Expand
PBW-degenerated Demazure modules and Schubert varieties for triangular elements
  • G. Fourier
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 2016
TLDR
These faces are normal polytopes and their Minkowski sum is compatible with tensor products, which implies that flat degenerations of the corresponding Schubert varieties to PBW degenerated and toric varieties are obtained. Expand
Transformation of Groups
In this work, we have proved a number of purely geometric statements by algebraic methods. Also we have proved Sylvester’s law of Nullity and Exercise: the nullity of the product BA never exceeds theExpand
Standard Monomial Theory and applications
In these notes, we explain how one can construct Standard Monomial Theory for reductive algebraic groups by using the path models of their representations and quantum groups at a root of unity. AsExpand
Res
12 AUTHORIZING THE AWARD OF A CONTRACT THROUGH A FAIR AND OPEN PROCESS IN ACCORDANCE WITH N.J.S.A. 19:44A‐20.5 ET SEQ. WITH MCAULIFFE & CARROLL ARCHITECTS, LLC, 439 SOUTH BROAD STREET, SUITE 310,Expand
SageMath
  • the Sage Mathematics Software System (Version 7.2),
  • 2016
IMRN
  • (15):6353–6374,
  • 2015
Zeitschrift
  • 287:615–654,
  • 2017
Zeitschrift
  • 287:615–654,
  • 2017
A
  • 139:132–152,
  • 2016
...
1
2
...