MONOMIAL REALIZATION OF THE CRYSTALS OVER U-q(A(infinity)) AND THE QUANTUM MONSTER ALGEBRA

초록

We give new realizations of the crystal bases of the Verma modules and the irreducible highest weight modules over the quantum generalized Kac-Moody algebra U-q(A(infinity)) and the quantum Monster algebra using Nakajima monomials. Moreover, another realization of the crystals B(infinity) and B(lambda) over U-q(A(infinity)) using triangular matrices and tableaux are given.

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