Alternating sign matrices and Verma modules

Hankyung Ko

Alternating sign matrices and Verma modules

Representation Theory 2021-08-18 v1 Combinatorics

Authors: Hankyung Ko

Abstract

We show that the poset of alternating sign matrices, with Bruhat order, is isomorphic to the poset of certain submodules of the dominant Verma module for the special linear Lie algebra $\frak{sl}_n$ . The latter poset consists of the intersections of Verma submodules and can also be defined in terms of a Kazhdan-Lusztig cell.

Keywords

lie algebras and modules kazhdan-lusztig theory highest weight modules

Cite

@article{arxiv.2108.07637,
  title  = {Alternating sign matrices and Verma modules},
  author = {Hankyung Ko},
  journal= {arXiv preprint arXiv:2108.07637},
  year   = {2021}
}

Comments

9 pages, 3 figures

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