PBW Bases and Marginally Large Tableaux in Types B and C

Jackson A. Criswell; Ben Salisbury; Peter Tingley

doi:10.4153/CMB-2017-071-1

PBW Bases and Marginally Large Tableaux in Types B and C

Jackson A. Criswell, Ben Salisbury, Peter Tingley

Department of Mathematics and Statistics

Central Michigan University

Research output: Contribution to journal › Article › peer-review

Abstract

We explicitly describe the isomorphism between two combinatorial realizations of Kashiwara’s infinity crystal in types B and C. The first realization is in terms of marginally large tableaux and the other is in terms of Kostant partitions coming from PBW bases. We also discuss a stack notation for Kostant partitions which simplifies that realization.

Original language	American English
Journal	Mathematics and Statistics: Faculty Publications and Other Works
Volume	62
Issue number	1
DOIs	https://doi.org/10.4153/CMB-2017-071-1
State	Published - Mar 1 2019

Keywords

crystal
Kostant Partition
Lusztig Data
marginally large tableau

Disciplines

Mathematics
Algebra
Discrete Mathematics and Combinatorics
Geometry and Topology

Access to Document

10.4153/CMB-2017-071-1License: Unspecified

PBW Bases and Marginally Large Tableaux in Types B and CFinal published version, 280 KBLicense: Unspecified

Cite this

@article{26124b8be3da42abab218d5ad3b9a5e4,

title = "PBW Bases and Marginally Large Tableaux in Types B and C",

abstract = " We explicitly describe the isomorphism between two combinatorial realizations of Kashiwara{\textquoteright}s infinity crystal in types B and C. The first realization is in terms of marginally large tableaux and the other is in terms of Kostant partitions coming from PBW bases. We also discuss a stack notation for Kostant partitions which simplifies that realization.",

keywords = "crystal, Kostant Partition, Lusztig Data, marginally large tableau",

author = "Criswell, \{Jackson A.\} and Ben Salisbury and Peter Tingley",

year = "2019",

month = mar,

day = "1",

doi = "10.4153/CMB-2017-071-1",

language = "American English",

volume = "62",

journal = "Mathematics and Statistics: Faculty Publications and Other Works",

number = "1",

}

TY - JOUR

T1 - PBW Bases and Marginally Large Tableaux in Types B and C

AU - Criswell, Jackson A.

AU - Salisbury, Ben

AU - Tingley, Peter

PY - 2019/3/1

Y1 - 2019/3/1

N2 - We explicitly describe the isomorphism between two combinatorial realizations of Kashiwara’s infinity crystal in types B and C. The first realization is in terms of marginally large tableaux and the other is in terms of Kostant partitions coming from PBW bases. We also discuss a stack notation for Kostant partitions which simplifies that realization.

AB - We explicitly describe the isomorphism between two combinatorial realizations of Kashiwara’s infinity crystal in types B and C. The first realization is in terms of marginally large tableaux and the other is in terms of Kostant partitions coming from PBW bases. We also discuss a stack notation for Kostant partitions which simplifies that realization.

KW - crystal

KW - Kostant Partition

KW - Lusztig Data

KW - marginally large tableau

UR - https://ecommons.luc.edu/math_facpubs/26

UR - http://arxiv.org/pdf/1708.04311.pdf

U2 - 10.4153/CMB-2017-071-1

DO - 10.4153/CMB-2017-071-1

M3 - Article

VL - 62

JO - Mathematics and Statistics: Faculty Publications and Other Works

JF - Mathematics and Statistics: Faculty Publications and Other Works

IS - 1

ER -

PBW Bases and Marginally Large Tableaux in Types B and C

Abstract

Keywords

Disciplines

Access to Document

Other files and links

Cite this