## 30 Citations

### Tau function of the CKP hierarchy and nonlinearizable virasoro symmetries

- Mathematics
- 2013

We introduce a single tau function that represents the C-type Kadomtsev–Petviashvili (CKP) hierarchy in a generalized Hirota ‘bilinear’ equation. The actions on the tau function by additional…

### Virasoro constraints for Drinfeld–Sokolov hierarchies and equations of Painlevé type

- Mathematics
- 2022

We construct a tau cover of the generalized Drinfeld–Sokolov hierarchy associated with an arbitrary affine Kac–Moody algebra with gradations s⩽1$\mathrm{s}\leqslant \mathbb {1}$ and derive its…

### Virasoro symmetries of Drinfeld-Sokolov hierarchies and equations of Painlev\'{e} type

- Mathematics
- 2019

We construct a tau cover of the generalized Drinfeld-Sokolov hierarchy associated to an arbitrary affine Kac-Moody algebra with gradations $\mathrm{s}\le\mathds{1}$ and derive its Virasoro…

### Virasoro constraints in Drinfeld–Sokolov hierarchies

- Mathematics
- 2013

We describe a geometric theory of Virasoro constraints in generalized Drinfeld–Sokolov hierarchies. Solutions of Drinfeld–Sokolov hierarchies are succinctly described by giving a principal bundle on…

### CMC hierarchy II: Non-commuting symmetries and affine Kac-Moody algebra

- Mathematics
- 2014

Continuing the previous work, we propose a further extension of the structure equation for a truncated CMC hierarchy by the non-commuting, truncated Virasoro algebra of non-local symmetries. Via a…

### Borodin–Okounkov formula, string equation and topological solutions of Drinfeld–Sokolov hierarchies

- MathematicsLetters in Mathematical Physics
- 2019

We give a general method to compute the expansion of topological tau functions for Drinfeld-Sokolov hierarchies associated to an arbitrary untwisted affine Kac-Moody algebra. Our method consists of…

### Drinfeld–Sokolov Hierarchies and Diagram Automorphisms of Affine Kac–Moody Algebras

- MathematicsCommunications in Mathematical Physics
- 2019

For a diagram automorphism of an affine Kac–Moody algebra such that the folded diagram is still an affine Dynkin diagram, we show that the associated Drinfeld–Sokolov hierarchy also admits an induced…

### Drinfeld–Sokolov Hierarchies and Diagram Automorphisms of Affine Kac–Moody Algebras

- MathematicsCommunications in Mathematical Physics
- 2019

For a diagram automorphism of an affine Kac–Moody algebra such that the folded diagram is still an affine Dynkin diagram, we show that the associated Drinfeld–Sokolov hierarchy also admits an induced…

### N ov 2 01 8 Drinfeld-Sokolov Hierarchies and Diagram Automorphisms of Affine Kac-Moody Algebras

- Mathematics
- 2018

For a diagram automorphism of an affine Kac-Moody algebra such that the folded diagram is still an affine Dynkin diagram, we show that the associated Drinfeld-Sokolov hierarchy also admits an induced…

### Simple Lie Algebras, Drinfeld–Sokolov Hierarchies, and Multi-Point Correlation Functions

- MathematicsMoscow Mathematical Journal
- 2021

For a simple Lie algebra $\mathfrak{g}$, we derive a simple algorithm for computing logarithmic derivatives of tau-functions of Drinfeld--Sokolov hierarchy of $\mathfrak{g}$-type in terms of…

## References

SHOWING 1-10 OF 51 REFERENCES

### Tau function of the CKP hierarchy and nonlinearizable virasoro symmetries

- Mathematics
- 2013

We introduce a single tau function that represents the C-type Kadomtsev–Petviashvili (CKP) hierarchy in a generalized Hirota ‘bilinear’ equation. The actions on the tau function by additional…

### Virasoro constraints in Drinfeld–Sokolov hierarchies

- Mathematics
- 2013

We describe a geometric theory of Virasoro constraints in generalized Drinfeld–Sokolov hierarchies. Solutions of Drinfeld–Sokolov hierarchies are succinctly described by giving a principal bundle on…

### A remark on Kac–Wakimoto hierarchies of D-type

- Mathematics
- 2009

For the Kac–Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra D(1)n, we compute the coefficients of the corresponding…

### Additional symmetries of generalized integrable hierarchies

- Mathematics
- 1993

The non-isospectral symmetries of a general class of integrable hierarchies are found by generalizing the Galilean and scaling symmetries of the Korteweg-de Vries equation and its hierarchy. The…

### On the Drinfeld–Sokolov Hierarchies of D Type

- Mathematics
- 2009

We extend the notion of pseudo-differential operators that are used to represent the Gelfand–Dickey hierarchies and obtain a similar representation for the full Drinfeld–Sokolov hierarchies of D n…

### Tau-Functions generating the Conservation Laws for Generalized Integrable Hierarchies of KdV and Affine-Toda type

- Mathematics
- 1999

### Generalized Drinfeld-Sokolov reductions and KdV type hierarchies

- Mathematics
- 1993

Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local reductions of Hamiltonian flows generated by monodromy invariants on the dual of a loop algebra. Following earlier work of…

### Generalized Drinfel'd-Sokolov hierarchies

- Mathematics
- 1992

A general approach is adopted to the construction of integrable hierarchies of partial differential equations. A series of hierarchies associated to untwisted Kac-Moody algebras, and conjugacy…