Generalized Young walls and crystal bases for quantum affine algebra of type 𝐴

Kim, Jeong-Ah; Shin, Dong-Uy

doi:10.1090/S0002-9939-2010-10428-8

Generalized Young walls and crystal bases for quantum affine algebra of type $A$
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by Jeong-Ah Kim and Dong-Uy Shin PDF

Proc. Amer. Math. Soc. 138 (2010), 3877-3889 Request permission

Abstract:

We give a new realization of the crystal $B(\infty )$ of $U_q^{-}(A_n^{(1)})$ using generalized Young walls, a modified notion of Young walls of type $A_n^{(1)}$. Moreover, by the fact that the irreducible highest weight crystal $B(\lambda )$ lies in the crystal $B(\infty )\otimes R_{\lambda }$, we construct the crystal $B(\lambda )$ using generalized Young walls.

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