Affine PBW bases and affine MV polytopes

被引：4
|
作者：
Muthiah, Dinakar [1 ]
Tingley, Peter [2 ]
机构：
[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA
[2] Loyola Univ, Dept Math & Stat, Chicago, IL 60611 USA
来源：
SELECTA MATHEMATICA-NEW SERIES | 2018年 / 24卷 / 05期
关键词：
Affine MV polytope; Quantum affine algebra; PBW basis; Crystal; MIRKOVIC-VILONEN POLYTOPES; BRAID GROUP ACTION; CANONICAL BASES; CRYSTAL BASES; RANK; ALGEBRAS; CONSTRUCTION;
D O I：
10.1007/s00029-018-0436-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show how affine PBW bases can be used to construct affine MV polytopes, and that the resulting objects agree with the affine MV polytopes recently constructed using either preprojective algebras or KLR algebras. To do this we first generalize work of Beck-Chari-Pressley and Beck-Nakajima to define affine PBW bases for arbitrary convex orders on positive roots. Our results describe how affine PBW bases for different convex orders are related, answering a question posed by Beck and Nakajima.
引用
收藏
页码：4781 / 4810
页数：30
相关论文
共 50 条
  • [1] Affine PBW bases and affine MV polytopes
    Dinakar Muthiah
    Peter Tingley
    [J]. Selecta Mathematica, 2018, 24 : 4781 - 4810
  • [2] Affine PBW bases and MV polytopes in rank 2
    Dinakar Muthiah
    Peter Tingley
    [J]. Selecta Mathematica, 2014, 20 : 237 - 260
  • [3] Affine PBW bases and MV polytopes in rank 2
    Muthiah, Dinakar
    Tingley, Peter
    [J]. SELECTA MATHEMATICA-NEW SERIES, 2014, 20 (01): : 237 - 260
  • [4] RANK 2 AFFINE MV POLYTOPES
    Baumann, Pierre
    Dunlap, Thomas
    Kamnitzer, Joel
    Tingley, Peter
    [J]. REPRESENTATION THEORY, 2013, 17 : 442 - 468
  • [5] MV-POLYTOPES VIA AFFINE BUILDINGS
    Ehrig, Michael
    [J]. DUKE MATHEMATICAL JOURNAL, 2010, 155 (03) : 433 - 482
  • [6] CONVEX BASES OF PBW TYPE FOR QUANTUM AFFINE ALGEBRAS
    BECK, J
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 165 (01) : 193 - 199
  • [7] THE PBW THEOREM FOR AFFINE YANGIANS
    Yang, Yaping
    Zhao, Gufang
    [J]. TRANSFORMATION GROUPS, 2020, 25 (04) : 1371 - 1385
  • [8] THE PBW THEOREM FOR AFFINE YANGIANS
    YAPING YANG
    GUFANG ZHAO
    [J]. Transformation Groups, 2020, 25 : 1371 - 1385
  • [9] A new description of convex bases of PBW type for untwisted quantum affine algebras
    Ito, Ken
    [J]. HIROSHIMA MATHEMATICAL JOURNAL, 2010, 40 (02) : 133 - 183
  • [10] PBW-bases of the twisted generic composition algebras of affine valued quivers
    Obul, A
    Zhang, GL
    [J]. JOURNAL OF ALGEBRA, 2006, 297 (02) : 333 - 360
12345