scholarly journals Quantum flag varieties, equivariant quantum D-modules, and localization of quantum groups

2006 ◽  
Vol 203 (2) ◽  
pp. 408-429 ◽  
Author(s):  
Erik Backelin ◽  
Kobi Kremnizer
Keyword(s):  
Quantum Groups ◽  
Flag Varieties

scholarly journals Cones from quantum groups to tropical flag varieties

2021 ◽  
Author(s):  
Xin Fang ◽  
Ghislain Fourier ◽  
Markus Reineke
Keyword(s):  
Quantum Groups ◽  
Flag Varieties ◽  
Quiver Representations ◽  
Canonical Bases ◽  
Enveloping Algebras ◽  
Quantized Enveloping Algebras

AbstractWe relate quantum degree cones, parametrizing PBW degenerations of quantized enveloping algebras, to (negative tight monomial) cones introduced by Lusztig in the study of monomials in canonical bases, to K-theoretic cones for quiver representations, and to some maximal prime cones in tropical flag varieties.

scholarly journals Curved Rickard complexes and link homologies

2020 ◽  
Vol 2020 (769) ◽  
pp. 87-119
Author(s):  
Sabin Cautis ◽  
Aaron D. Lauda ◽  
Joshua Sussan
Keyword(s):  
Spectral Sequence ◽  
Quantum Groups ◽  
Braid Group ◽  
Derived Categories ◽  
Duke Math ◽  
Khovanov Homology ◽  
Hilbert Schemes ◽  
Coherent Sheaves ◽  
Knot Homology ◽  
Original Motivation

AbstractRickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to obtain deformations of link homologies which generalize those of Batson–Seed [3] [J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 2015, 5, 801–841] and Gorsky–Hogancamp [E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint 2017] to arbitrary representations/partitions. Another is to relate the deformed homology defined algebro-geometrically in [S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, colored links, Quantum Topol. 8 2017, 2, 381–411] to categorified quantum groups (this was the original motivation for this paper).

Tropical flag varieties

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

scholarly journals Bialgebra cohomology, deformations, and quantum groups.

1990 ◽  
Vol 87 (1) ◽  
pp. 478-481 ◽  
Author(s):  
M. Gerstenhaber ◽  
S. D. Schack
Keyword(s):  
Quantum Groups
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