The Crystal${\cal B}$(∞) and Extended Nakajima Monomials

The Crystal${\cal B}$(∞) and Extended Nakajima Monomials

We construct the set of extended Nakajima monomials containing monomials realizing the irreducible highest weight crystals, introduced by Nakajima. We present explicit descriptions of a crystal ${\cal B}_{\infty}$ and the crystal ${\cal B}$(∞) in this language for the case $A_{n}^{(1)}$.

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Veröffentlicht in:Proceedings of the American Mathematical Society 2009-06, Vol.137 (6), p.1915-1924
1. Verfasser: Lee, Hyeonmi
Format: Artikel
Sprache:eng
Schlagworte:
Abstracting
Algebra
Crystal structure
Crystals
Integers
Isomorphism
Tableaux
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Zusammenfassung:We construct the set of extended Nakajima monomials containing monomials realizing the irreducible highest weight crystals, introduced by Nakajima. We present explicit descriptions of a crystal ${\cal B}_{\infty}$ and the crystal ${\cal B}$(∞) in this language for the case $A_{n}^{(1)}$.
ISSN:0002-9939
1088-6826