Using Nakajima’s monomials, we construct a new realization of crystal bases for ﬁnite dimensional irreducible modules over quantum classical algebras. We also give an explicit bijection between the monomial realization and the Young tableau realization of crystal bases.
Cite this article
Seok-Jin Kang, Dong-Uy Shin, Jeong-Ah Kim, Crystal Bases for Quantum Classical Algebras and Nakajima’s Monomials. Publ. Res. Inst. Math. Sci. 40 (2004), no. 3, pp. 757–791DOI 10.2977/PRIMS/1145475492