$$\underline{p}$$ p ̲ -reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$ W -algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ W ( gl N , p ̲ )
Abstract For each partition $$\underline{p}$$ p ̲ of an integer...
| Main Authors: | , , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
|
| Online Access: | https://hdl.handle.net/1721.1/131852 |
| Summary: | 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. |
|---|