Poisson Structures for Dispersionless Integrable Systems and Associated W-Algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Poisson Structures for Dispersionless Integrable Systems and Associated W-Algebras

Authors:	Cheng Yi Li Zhifeng

Affiliation:	(1) Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China. e-mail;(2) Nonlinear Science Center, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China

Abstract:	In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators $L = p^n + sumnolimits_{j = - infty }^{n - 1} {u_j p^j }$ . The reduction of the Poisson structure to the symplectic submanifold $u_{n - 1} = 0$ gives rise to W-algebras. In this Letter, we discuss properties of this Poisson structure, its Miura transformation and reductions. We are particularly interested in the following two cases: (a) L is pure polynomial in p with multiple roots and (b) L has multiple poles at finite distance. The w-algebra corresponding to the case (a) is defined as ${text{w}}_{left[ {m_1 ,m_2 , cdot cdot cdot ,m_r } right]}$ , where means the multiplicity of roots and to the case (b) is defined by ${text{w}}left( {n,left[ {m_1 ,m_2 , cdot cdot cdot ,m_r } right]}right)$ where is the multiplicity of poles. We prove that ${text{w}}left( {n,left[ {m_1 ,m_2 , cdot cdot cdot ,m_r } right]}right)$ -algebra is isomorphic via a transformation to ${text{W}}_{left[ {m_i ,m_2 , cdot cdot cdot ,m_r } right]}$ ${text{w}}_{n + m}$ U(1) with m= . We also give the explicit free fields representations for these W-algebras.

Keywords:	Poisson structure Miura transformation w-algebra.
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