TY - JOUR
T1 - Generalized Young Walls for Classical Lie Algebras
AU - Kim, Jeong Ah
AU - Shin, Dong Uy
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media B.V., part of Springer Nature.
PY - 2019/4/15
Y1 - 2019/4/15
N2 - In this paper, we introduce an new combinatorial model, which we call generalized Young walls for classical Lie algebras, and we give two realizations of the crystal B(∞) over classical Lie algebras using generalized Young walls. Also, we construct natural crystal isomorphisms between generalized Young wall realizations and other realizations, for example, monomial realization, polyhedral realization and tableau realization. Moreover, as applications, we obtain a crystal isomorphism between two different polyhedral realizations of B(∞).
AB - In this paper, we introduce an new combinatorial model, which we call generalized Young walls for classical Lie algebras, and we give two realizations of the crystal B(∞) over classical Lie algebras using generalized Young walls. Also, we construct natural crystal isomorphisms between generalized Young wall realizations and other realizations, for example, monomial realization, polyhedral realization and tableau realization. Moreover, as applications, we obtain a crystal isomorphism between two different polyhedral realizations of B(∞).
KW - Crystals
KW - Generalized Young walls
KW - Kashiwara embeddings
KW - Nakajima monomials
KW - Tableaux
UR - http://www.scopus.com/inward/record.url?scp=85045076662&partnerID=8YFLogxK
U2 - 10.1007/s10468-018-9770-z
DO - 10.1007/s10468-018-9770-z
M3 - Article
AN - SCOPUS:85045076662
SN - 1386-923X
VL - 22
SP - 345
EP - 373
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
IS - 2
ER -