Dong-Uy Shin

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We prove that the multiplicity of an arbitrary dominant weight for an integrable highest weight representation of the affine Kac-Moody algebra A (1) r is a polynomial in the rank r. In the process we show that the degree of this polynomial is less than or equal to the depth of the weight with respect to the highest weight. These results allow weight(More)
We give a 1-1 correspondence with the Young wall realization and the Young tableau realization of the crystal bases for the classical Lie algebras. Introduction Young tableaux and Young walls play important roles in the interplay, which can be explained in a beautiful manner using the crystal base theory for quantum groups, between the fields of(More)
In this paper, we give a new realization of crystal bases for irreducible highest weight modules over Uq(G2) in terms of monomials. We also discuss the natural connection between the monomial realization and tableau realization. Introduction In 1985, the quantum groups Uq(g), which may be thought of as q-deformations of the universal enveloping algebras(More)
  • 2007
Fix integers q, g, k, d. Set πd,k,q := kd − d − k + kq + 1 and assume q > 0, k ≥ 2, d ≥ 3q + 1, g ≥ kq − k + 1 and πd,k,q − ((⌊d/2⌋ + 1 − q) · (⌊k/2⌋ + 1) ≤ g ≤ πd,k,q. Let Y be a smooth and connected genus q projective curve. Here we prove the existence of a smooth and connected genus g projective curve X, a degree k morphism f : X → Y and a degree d(More)
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