A new Young wall realization of $B(λ)$ and $B(\infty)$

Fuente: arXiv
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Main Authors: Fan, Zhaobing, Han, Shaolong, Kang, Seok-Jin, Kim, Young Rock
Format: Preprint
Published: 2024
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author Fan, Zhaobing
Han, Shaolong
Kang, Seok-Jin
Kim, Young Rock
author_facet Fan, Zhaobing
Han, Shaolong
Kang, Seok-Jin
Kim, Young Rock
contents Using new combinatorics of Young walls, we give a new construction of the arbitrary level highest weight crystal $B(λ)$ for the quantum affine algebras of types $A^{(2)}_{2n}$, $D^{(2)}_{n+1}$, $A^{(2)}_{2n-1}$, $D^{(1)}_n$, $B^{(1)}_n$ and $C^{(1)}_n$. We show that the crystal consisting of reduced Young walls is isomorphic to the crystal $B(λ)$. Moreover, we provide a new realization of the crystal $B(\infty)$ in terms of reduced virtual Young walls and reduced extended Young walls.
format Preprint
id arxiv_https___arxiv_org_abs_2403_11055
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A new Young wall realization of $B(λ)$ and $B(\infty)$
Fan, Zhaobing
Han, Shaolong
Kang, Seok-Jin
Kim, Young Rock
Quantum Algebra
Combinatorics
Representation Theory
Using new combinatorics of Young walls, we give a new construction of the arbitrary level highest weight crystal $B(λ)$ for the quantum affine algebras of types $A^{(2)}_{2n}$, $D^{(2)}_{n+1}$, $A^{(2)}_{2n-1}$, $D^{(1)}_n$, $B^{(1)}_n$ and $C^{(1)}_n$. We show that the crystal consisting of reduced Young walls is isomorphic to the crystal $B(λ)$. Moreover, we provide a new realization of the crystal $B(\infty)$ in terms of reduced virtual Young walls and reduced extended Young walls.
title A new Young wall realization of $B(λ)$ and $B(\infty)$
topic Quantum Algebra
Combinatorics
Representation Theory
url https://arxiv.org/abs/2403.11055