A generalization of adjoint crystals for the quantized affine algebras of type $A\sb{n}\sp{(1)}$, $C\sb{n}\sp{(1)}$ and $D\sb{n+1}\sp{(2)}$

TL;DR

This paper extends the concept of adjoint crystals to a broader class of quantized affine algebras, specifically types A, C, and D, providing a unified crystal structure description.

Contribution

It generalizes the existing adjoint crystals framework to new affine types, offering a comprehensive description of their crystal structures.

Findings

Unified crystal structures for types A, C, D affine algebras.

Extension of adjoint crystals beyond original types.

New combinatorial models for these crystals.

Abstract

We propose to generalize Benkart-Frenkel-Kang-Lee's adjoint crystals and describe their crystal structure for type $A\sb{n}\sp{(1)}$, $C\sb{n}\sp{(1)}$ and $D\sb{n+1}\sp{(2)}$.