$$\underline{p}$$ 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 |
| _version_ | 1826215482929184768 |
|---|---|
| author | Carpentier, Sylvain De Sole, Alberto Kac, Victor G Valeri, Daniele van de Leur, Johan |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Carpentier, Sylvain De Sole, Alberto Kac, Victor G Valeri, Daniele van de Leur, Johan |
| author_sort | Carpentier, Sylvain |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T16:31:13Z |
| format | Article |
| id | mit-1721.1/131852 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:31:13Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1318522024-01-05T16:20:39Z $$\underline{p}$$ p ̲ -reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$ W -algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ W ( gl N , p ̲ ) Carpentier, Sylvain De Sole, Alberto Kac, Victor G Valeri, Daniele van de Leur, Johan Massachusetts Institute of Technology. Department of Mathematics 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. 2021-09-20T17:30:38Z 2021-09-20T17:30:38Z 2020-08-04 2020-11-04T04:25:28Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131852 en https://doi.org/10.1007/s00220-020-03817-x Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Carpentier, Sylvain De Sole, Alberto Kac, Victor G Valeri, Daniele van de Leur, Johan $$\underline{p}$$ p ̲ -reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$ W -algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ W ( gl N , p ̲ ) |
| title | $$\underline{p}$$ p ̲ -reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$ W -algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ W ( gl N , p ̲ ) |
| title_full | $$\underline{p}$$ p ̲ -reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$ W -algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ W ( gl N , p ̲ ) |
| title_fullStr | $$\underline{p}$$ p ̲ -reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$ W -algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ W ( gl N , p ̲ ) |
| title_full_unstemmed | $$\underline{p}$$ p ̲ -reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$ W -algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ W ( gl N , p ̲ ) |
| title_short | $$\underline{p}$$ p ̲ -reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$ W -algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ W ( gl N , p ̲ ) |
| title_sort | underline p p ̲ reduced multicomponent kp hierarchy and classical mathcal w w algebras mathcal w mathfrak gl n underline p w gl n p ̲ |
| url | https://hdl.handle.net/1721.1/131852 |
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