ﻻ يوجد ملخص باللغة العربية
We construct a Young wall model for higher level $A_2^{(2)}$-type adjoint crystals. The Young walls and reduced Young walls are defined in connection with affin energy function. We prove that the affine crystal consisiting of reduced Young walls provides a realization of highest weight crystals $B(lambda)$ and $B(infty)$.
We present sum-sides for principal characters of all standard (i.e., integrable and highest-weight) irreducible modules for the affine Lie algebra $A_2^{(2)}$. We use modifications of five known Bailey pairs; three of these are sufficient to obtain a
In this paper, we develop the theory of abstract crystals for quantum Borcherds-Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crystal embedding theorem and provide a characterization of ${B}(infty)$
The crystals for a finite-dimensional complex reductive Lie algebra $mathfrak{g}$ encode the structure of its representations, yet can also reveal surprising new structure of their own. We study the cactus group $C_{mathfrak{g}}$, constructed using t
The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this transform
We construct an explicit algorithm of the static-preserving bijection between the rigged configurations and the highest weight paths of the form $(B^{2,1})^{otimes L}$ in the $G_{2}^{(1)}$ adjoint crystals.