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Twisted Vertex Operators and Unitary Lie Algebras
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- Journal:
- Canadian Journal of Mathematics / Volume 67 / Issue 3 / 01 June 2015
- Published online by Cambridge University Press:
- 20 November 2018, pp. 573-596
- Print publication:
- 01 June 2015
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- Article
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A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral
${{\mathbb{Z}}_{2}}$-lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac–Moody Lie algebra of type 
$A_{n}^{\left( 2 \right)}$ are recovered by the new method.
On smooth solutions to the initial value problem for the mixed nonlinear Schrödinger equations*
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- Journal:
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics / Volume 119 / Issue 1-2 / 1991
- Published online by Cambridge University Press:
- 14 November 2011, pp. 31-45
- Print publication:
- 1991
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Solutions to the initial value problem for the mixed nonlinear Schrödinger equation
are considered. Conditions on the constants α,β, γ, function g(·) and initial data u(x, 0) are given so that, for this problem, the unique existence of smooth solutions is proved. In addition, the decay behaviours of the smooth solutions as |x|→+∞ are discussed.
