Cones from quantum groups to tropical flag varieties
نویسندگان
چکیده
Abstract We relate quantum degree cones, parametrizing PBW degenerations of quantized enveloping algebras, to (negative tight monomial) cones introduced by Lusztig in the study monomials canonical bases, K -theoretic for quiver representations, and some maximal prime tropical flag varieties.
منابع مشابه
Loop Groups and Their Flag Varieties
1. Reductive groups over local fields 1 1.1. Reductive groups over a field 1 1.2. The apartment of a reductive group over a local field 4 1.3. The existence of valuations of a root datum 12 1.4. The Bruhat-Tits group schemes 17 2. Loop groups 24 2.1. Definition of loop groups 24 2.2. The loop group of Ga and Gm 27 2.3. The loop groups of tori 30 2.4. Subgroups of LG 33 2.5. Integral models of L...
متن کامل“CLASSICAL” FLAG VARIETIES FOR QUANTUM GROUPS: THE STANDARD QUANTUM SL(n,C)
We suggest a possible programme to associate geometric “flaglike” data to an arbitrary simple quantum group, in the spirit of the noncommutative algebraic geometry developed by Artin, Tate, and Van den Bergh. We then carry out this programme for the standard quantum SL(n) of Drinfeld and Jimbo, where the varieties involved are certain T -stable subvarieties of the (ordinary) flag variety.
متن کاملThe Quantum Cohomology Ring of Flag Varieties
We describe the small quantum cohomology ring of complete flag varieties by algebro-geometric methods, as presented in our previous work Quantum cohomology of flag varieties (Internat. Math. Res. Notices, no. 6 (1995), 263–277). We also give a geometric proof of the quantum Monk formula.
متن کاملExamples of quantum cluster algebras associated to partial flag varieties
We give several explicit examples of quantum cluster algebra structures, as introduced by Berenstein and Zelevinsky, on quantized coordinate rings of partial flag varieties and their associated unipotent radicals. These structures are shown to be quantizations of the cluster algebra structures found on the corresponding classical objects by Geiß, Leclerc and Schröer, whose work generalizes that...
متن کاملPhylogenetic trees and the tropical geometry of flag varieties
We will discuss some recent theorems relating the space of weighted phylogenetic trees to the tropical varieties of each flag variety of type A. We will also discuss the tropicalizations of the functions corresponding to semi-standard tableaux, in particular we relate them to familiar functions from phylogenetics. We close with some remarks on the generalization of these results to the tropical...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2021
ISSN: ['0925-9899', '1572-9192']
DOI: https://doi.org/10.1007/s10801-021-01022-0