Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CRYSTAL B(λ) IN B(∞) FOR G2 TYPE LIE ALGEBRA

  • Kim, Min Kyu (Department of Mathematics Education Gyeongin National University of Education) ;
  • Lee, Hyeonmi (Department of Mathematics and Research Institute for Natural Sciences Hanyang University)
  • Received : 2013.10.23
  • Accepted : 2014.01.18
  • Published : 2014.03.01
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Abstract

A previous work gave a combinatorial description of the crystal B(${\infty}$), in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Using this result, we present an explicit description of the crystal B(${\lambda}$), in terms of the marginally large tableaux, for the $G_2$ Lie algebra type. We also provide a new description of B(${\lambda}$), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.

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References

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