Saved in:
Bibliographic Details
Main Author: Zhang, Sylvester W.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2409.20389
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910625380171776
author Zhang, Sylvester W.
author_facet Zhang, Sylvester W.
contents We show that the Hilbert space with basis indexed by infinite permutations and the cohomology ring of the infinite flag variety can be seen as representations of the Heisenberg algebra, which are isomorphic using the back-stable Schubert polynomials. We give a model for infinite permutations as certain two dimensional fermions, generalizing the Maya diagram construction for partitions. Under this framework, the pipedream model for Schubert polynomials can be viewed as the Hamiltonian time evolution of the 2D fermions.
format Preprint
id arxiv_https___arxiv_org_abs_2409_20389
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Schubert Calculus and the Heisenberg Algebra
Zhang, Sylvester W.
Combinatorics
05e05, 14N15, 81R10
We show that the Hilbert space with basis indexed by infinite permutations and the cohomology ring of the infinite flag variety can be seen as representations of the Heisenberg algebra, which are isomorphic using the back-stable Schubert polynomials. We give a model for infinite permutations as certain two dimensional fermions, generalizing the Maya diagram construction for partitions. Under this framework, the pipedream model for Schubert polynomials can be viewed as the Hamiltonian time evolution of the 2D fermions.
title Schubert Calculus and the Heisenberg Algebra
topic Combinatorics
05e05, 14N15, 81R10
url https://arxiv.org/abs/2409.20389