The Hidden Kac-Moody Symmetry of the Geometric Actions

Aratyn, H.; Nissimov, Emil; Pacheva, Svetlana

doi:10.1142/s0217732390002912

Cited by 27 publications

(119 citation statements)

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“…For bosonic SKP (R;M B ,M F ) hierarchies (33) we obtain similar results with (255) and (256) replaced by:…”

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confidence: 73%

“…[21] where the latter problem has been solved via appropriate modification of the standard additional-symmetry generating Orlov-Schulman operators. In fact, we will construct here the Virasoro additional symmetries for bosonic constrained SKP (R;M B ,M F ) hierarchies (33). This same construction based on the super-pseudo-differential formalism does not, however, carry over to the case of the fermionic part of the full super-Virasoro and the rest of super-W 1+∞ symmetries, as well to the case of (super-)Virasoro and super-W 1+∞ symmetries for fermionic constrained SKP (R;M B ,M F ) hierarchies (24).…”

Section: Virasoro Symmetries Of Constrained Skp Hierarchiesmentioning

confidence: 99%

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Symmetries of supersymmetric integrable hierarchies of KP type

Nissimov

Pacheva

2002

Journal of Mathematical Physics

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This paper is devoted to the systematic study of additional (non-isospectral) symmetries of constrained (reduced) supersymmetric integrable hierarchies of KP type -the so called SKP (R;MB ,MF ) models. The latter are supersymmetric extensions of ordinary constrained KP hierarchies which contain as special cases basic integrable systems such as (m)KdV, AKNS, FordyKulish, Yajima-Oikawa etc.. As a first main result it is shown that any SKP (R;MB ,MF ) hierarchy possesses two different mutually (anti-)commuting types of superloop superalgebra additional symmetries corresponding to the positive-grade and negative-grade parts of certain superloop superalgebras. The second main result is the systematic construction of the full algebra of additional Virasoro symmetries of SKP (R;MB ,MF ) hierarchies, which requires non-trivial modifications of the Virasoro flows known from the general case of unconstrained Manin-Radul super-KP hierarchies (the latter flows do not define symmetries for constrained SKP (R;MB ,MF ) hierarchies). As a third main result we provide systematic construction of the supersymmetric analogues of multi-component (matrix) KP hierarchies and show that the latter contain among others the supersymmetric version of Davey-Stewartson system. Finally, we present an explicit derivation of the general Darboux-Bäcklund solutions for the SKP (R;MB ,MF ) super-tau functions (supersymmetric "soliton"-like solutions) which preserve the additional (non-isospectral) symmetries.

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“…For bosonic SKP (R;M B ,M F ) hierarchies (33) we obtain similar results with (255) and (256) replaced by:…”

supporting

confidence: 73%

Section: Virasoro Symmetries Of Constrained Skp Hierarchiesmentioning

confidence: 99%

Symmetries of supersymmetric integrable hierarchies of KP type

Nissimov

Pacheva

2002

Journal of Mathematical Physics

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“…and appropriate scaling of the variables x and t. Recently, there has been a lot of interest in this system [6][7][8][9][10] from various points of view. The construction of the Gelfand-Dikii brackets for such systems is, therefore, of significance.…”

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confidence: 99%

Gelfand-Dikii Brackets for Nonstandard Lax Equations

1994

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“…which is a special two-boson case of the system (10)- (11). We now introduce an useful concept of a square-lattice.…”

Section: Multi-boson Lattice Systems and The Bäcklund Transformationsmentioning

confidence: 99%

On discrete symmetries of the multi-boson KP hierarchies

1994

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We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to the discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This establishes a canonical nature of the discrete transformations. The spectral equation, which defines both the lattice system and the corresponding Lax operator, plays a key role in determining pertinent symmetry structure.We also introduce a concept of the square-root lattice leading to a family of new pseudodifferential operators with covariance under additional Bäcklund transformations.

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The Hidden Kac-Moody Symmetry of the Geometric Actions

Cited by 27 publications

References 0 publications

Symmetries of supersymmetric integrable hierarchies of KP type

Symmetries of supersymmetric integrable hierarchies of KP type

Gelfand-Dikii Brackets for Nonstandard Lax Equations

On discrete symmetries of the multi-boson KP hierarchies

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