khive-crystal
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Repository
Basic Info
- Host: GitHub
- Owner: snrsw
- Language: Python
- Default Branch: master
- Size: 281 KB
Statistics
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
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Metadata Files
README.md
khive-crystal
This repository contains the experimetns code for our paper Algorithms for crystal structure on K-hives of type A.
Documentation
- https://snrsw.github.io/khive-crystal/khive_crystal/
Overview
Let $\mathfrak{g}$ be a Lie algebra of type $A_{n-1}$. Let $P^+$ be a set of dominant integral weights of $\mathfrak{g}$. For $\lambda \in P^+$, let $\mathbb{H}(\lambda)$ be a set of K-hives which right edge labels is determied by $\lambda$.
khive-crystal compute the crystal structure on $\mathbb{H}(\lambda)$.
Getting started
Install
bash
pip install khive-crystal
Usage
For more information, see https://snrsw.github.io/khive-crystal/
K-hive
```python
from khive_crystal import khive khive(alpha=[2, 1, 0], beta=[2, 1, 0], gamma=[0, 0, 0], Uij=[[0, 0], [0]]) KHive(alpha=[2, 1, 0], beta=[2, 1, 0], gamma=[0, 0, 0], Uij=[[0, 0], [0]]) ```
```python
from khive_crystal import khive, view view(khive(alpha=[2, 1, 0], beta=[2, 1, 0], gamma=[0, 0, 0], Uij=[[0, 0], [0]])) ```
.png)
Crystal structure
$\mathbb{H}(\Lambda_k)$
For $k = 1, 2, \dots, n-1$, let $\Lambdak$ be the fundamental weight of $\mathfrak{g}$. The crystal structure on $\mathbb{H}(\Lambdak)$ is computed as follows.
```python
from khivecrystal.khive import KHive from khivecrystal import khive, view, f, phi, e, epsilon H: KHive = khive( ... n=3, ... alpha=[1, 1, 0], ... beta=[1, 1, 0], ... gamma=[0, 0, 0], ... Uij=[[0, 0], [0]] ... ) # alpha = \Lambda_2 phi(i=2)(H) 1 f(i=2)(H) KHive(alpha=[1, 1, 0], beta=[1, 0, 1], gamma=[0, 0, 0], Uij=[[0, 0], [1]]) epsilon(i=2)(H) 0 e(i=2)(H)
None
```
$\mathbb{H}(\lambda)$
Let $\lambda \in P^+$. The crystal structure on $\mathbb{H}(\lambda)$ is computed in two ways.
As a submodule of tensor products of $\mathbb{H}(\Lambda_k)$
The crystal structure on $\mathbb{H}(\lambda)$ is determined such that the map $\Psi \colon \mathbb{H}(\lambda) \to \bigotimes{k} \mathbb{H}(\Lambdak)$ is a crystal embedding.
```python
from khivecrystal.khive import KHive from khivecrystal import khive, view, f, phi, e, epsilon, psi, psilambda, psiinv H: KHive = khive(n=3, alpha=[3, 1, 0], beta=[2, 2, 0], gamma=[0, 0, 0], Uij=[[1, 0], [0]]) psilambda(H=H) [KHive(alpha=[2, 0, 0], beta=[1, 1, 0], gamma=[0, 0, 0], Uij=[[1, 0], [0]]), KHive(alpha=[1, 1, 0], beta=[1, 1, 0], gamma=[0, 0, 0], Uij=[[0, 0], [0]])] psi(H=H) [KHive(alpha=[1, 0, 0], beta=[0, 1, 0], gamma=[0, 0, 0], Uij=[[1, 0], [0]]), KHive(alpha=[1, 0, 0], beta=[1, 0, 0], gamma=[0, 0, 0], Uij=[[0, 0], [0]]), KHive(alpha=[1, 1, 0], beta=[1, 1, 0], gamma=[0, 0, 0], Uij=[[0, 0], [0]])] psiinv( ... H=f(i=1)( ... psi( ... H=H ... ) ... ) ... ) KHive(alpha=[3, 1, 0], beta=[1, 3, 0], gamma=[0, 0, 0], Uij=[[2, 0], [0]]) ```
Explicit method
```python
from khive_crystal import khive, view, f, phi, e, epsilon H: KHive = khive(n=3, alpha=[3, 1, 0], beta=[2, 2, 0], gamma=[0, 0, 0], Uij=[[1, 0], [0]]) f(i=2)(H) KHive(alpha=[3, 1, 0], beta=[1, 3, 0], gamma=[0, 0, 0], Uij=[[2, 0], [0]]) ```
Crystal graph
```python
from khivecrystal import khives, crystalgraph crystal_graph(khives(n=3, alpha=[2, 1, 0])) ```
.png)
Owner
- Login: snrsw
- Kind: user
- Repositories: 4
- Profile: https://github.com/snrsw
Citation (CITATION.cff)
# This CITATION.cff file was generated with cffinit.
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cff-version: 1.2.0
title: khive-crystal
message: >-
If you use this software, please cite it using the
metadata from this file.
type: software
authors:
- given-names: Shota
family-names: Narisawa
email: ale.nnn.r@gmail.com
url: https://github.com/snrsw/khive-crystal
version: 0.1.0
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Last synced: 10 months ago
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- snrsw (32)
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- Total packages: 1
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Total downloads:
- pypi 9 last-month
- Total dependent packages: 0
- Total dependent repositories: 0
- Total versions: 1
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pypi.org: khive-crystal
Add your description here
- Documentation: https://khive-crystal.readthedocs.io/
-
Latest release: 0.1.0
published over 1 year ago