Weighted PBW degenerations and tropical flag varieties-Reference-Cited by-同舟云学术

Weighted PBW degenerations and tropical flag varieties

Published:2019-01-28 Issue:01 Volume:21 Page:1850016
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Fang X.¹,Feigin E.²³,Fourier G.⁴,Makhlin I.³⁵

Affiliation:

1. Mathematical Institute, University of Cologne, Weyertal 86–90, 50931, Cologne, Germany

2. Department of Mathematics, National Research University Higher School of Economics, Usacheva str. 6, 119048, Moscow, Russia

3. Skolkovo Institute of Science and Technology, Nobelya Ulitsa 3, Moscow 121205, Russia

4. Institute for Algebra, Number Theory and Discrete Mathematics, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany

5. International Laboratory of Representation Theory and Mathematical Physics, National Research University Higher School of Economics, Usacheva str. 6, 119048, Moscow, Russia

Abstract

We study algebraic, combinatorial and geometric aspects of weighted Poincaré–Birkhoff–Witt (PBW)-type degenerations of (partial) flag varieties in type [Formula: see text]. These degenerations are labeled by degree functions lying in an explicitly defined polyhedral cone, which can be identified with a maximal cone in the tropical flag variety. Varying the degree function in the cone, we recover, for example, the classical flag variety, its abelian PBW degeneration, some of its linear degenerations and a particular toric degeneration.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199718500165

Reference21 articles.

1. Toric degenerations of spherical varieties

2. Okounkov bodies and toric degenerations

3. Computing Toric Degenerations of Flag Varieties

4. Lie Algebras of Finite and Affine Type

5. Linear degenerations of flag varieties

Cited by 10 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Beyond the Sottile–Sturmfels Degeneration of a Semi-Infinite Grassmannian;International Mathematics Research Notices;2022-05-24

2. SYMPLECTIC PBW DEGENERATE FLAG VARIETIES; PBW TABLEAUX AND DEFINING EQUATIONS;Transformation Groups;2022-03-31

3. Exact structures and degeneration of Hall algebras;Advances in Mathematics;2022-03

4. Gröbner fans of Hibi ideals, generalized Hibi ideals and flag varieties;Journal of Combinatorial Theory, Series A;2022-01

5. The Tropical Symplectic Grassmannian;International Mathematics Research Notices;2021-10-08