$$\underline{p}$$ p ̲ -reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$ W -algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ W ( gl N , p ̲ )
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Author(s)
Carpentier, Sylvain
De Sole, Alberto
Kac, Victor G
Valeri, Daniele
van de Leur, Johan
Date Issued
August 4, 2020
Publisher
Springer Berlin Heidelberg
Version
Author's final manuscript
Abstract
Abstract
For each partition
$$\underline{p}$$
p
̲
of an integer
$$N\ge 2$$
N
≥
2
, consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present paper we show that any tau-function of the
$$\underline{p}$$
p
̲
-reduced r-component KP hierarchy produces a solution of this integrable hierarchy. Along the way we provide an algorithm for the explicit construction of the generators of the corresponding classical
$$\mathcal {W}$$
W
-algebra
$$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$
W
(
gl
N
,
p
̲
)
, and write down explicit formulas for evolution of these generators along the commuting Hamiltonian flows.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00220-020-03817-x
