Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-08-05
Commun.Math.Phys. 175 (1996) 177-202
Physics
High Energy Physics
High Energy Physics - Theory
26p, latex, BONN--TH-94-17, SISSA-ISAS-118/94/EP, AS-ITP-94-43, revised version with additions
Scientific paper
10.1007/BF02101629
For any two arbitrary positive integers `$n$' and `$m$', using the $m$--th KdV hierarchy and the $(n+m)$--th KdV hierarchy as building blocks, we are able to construct another integrable hierarchy (referred to as the $(n,m)$--th KdV hierarchy). The $W$--algebra associated to the \shs\, of the $(n,m)$--th KdV hierarchy (called $W(n,m)$ algebra) is isomorphic via a Miura map to the direct sum of $W_m$--algebra, $W_{n+m}$--algebra and an additional $U(1)$ current algebra. In turn, from the latter, we can always construct a representation of $W_\infty$--algebra.
Bonora Loriano
Liu Qing-Ping
Xiong Chuan-Sheng
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