The Kp Hierarchy

1989 ◽  
pp. 245-265
Author(s):  
Jouko Mickelsson
Keyword(s):  
Kp Hierarchy

scholarly journals Genus expansion of matrix models and ћ expansion of KP hierarchy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Special Interest ◽  
Hermitian Matrix ◽  
Geometric Meaning ◽  
Kp Hierarchy ◽  
Hurwitz Numbers ◽  
Kp Equations ◽  
Genus Expansion ◽  
Hermitian Matrix Model

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

scholarly journals Intertwining operator and integrable hierarchies from topological strings

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jean-Emile Bourgine
Keyword(s):  
Topological Strings ◽  
Vertex Operator ◽  
Integrable Hierarchies ◽  
Kp Hierarchy ◽  
Tau Function ◽  
Time Deformation ◽  
Toroidal Algebra ◽  
Crystal Model ◽  
Melting Crystal ◽  
Definition Of

Abstract In [1], Nakatsu and Takasaki have shown that the melting crystal model behind the topological strings vertex provides a tau-function of the KP hierarchy after an appropriate time deformation. We revisit their derivation with a focus on the underlying quantum W1+∞ symmetry. Specifically, we point out the role played by automorphisms and the connection with the intertwiner — or vertex operator — of the algebra. This algebraic perspective allows us to extend part of their derivation to the refined melting crystal model, lifting the algebra to the quantum toroidal algebra of $$ \mathfrak{gl} $$ gl (1) (also called Ding-Iohara-Miki algebra). In this way, we take a first step toward the definition of deformed hierarchies associated to A-model refined topological strings.

scholarly journals The KP hierarchy in Miwa coordinates

1999 ◽  
Vol 258 (4-6) ◽  
pp. 272-278 ◽  
Author(s):  
Boris Konopelchenko ◽  
Luis Martı́nez Alonso
Keyword(s):  
Kp Hierarchy

Darboux transformations and Darboux coverings: some applications to the KP hierarchy

1998 ◽  
Vol 15 (4) ◽  
Author(s):  
Paolo Casati ◽  
GREGORIO Falqui ◽  
FRANCO Magri ◽  
Marco Pedroni ◽  
Jorge Zubelli
Keyword(s):  
Darboux Transformations ◽  
Kp Hierarchy

Recursion relations for the constrained multi-component KP hierarchy

2017 ◽  
Vol 33 (11) ◽  
pp. 1578-1586
Author(s):  
Xu Gao ◽  
Chuan Zhong Li ◽  
Jing Song He
Keyword(s):  
Kp Hierarchy ◽  
Recursion Relations

scholarly journals The super W∞ symmetry of the Manin-Radul super KP hierarchy

1992 ◽  
Vol 277 (4) ◽  
pp. 435-441 ◽  
Author(s):  
A. Das ◽  
E. Sezgin ◽  
S.J. Sin
Keyword(s):  
Kp Hierarchy
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