Solutions of the universal character hierarchy and BUC hierarchy by fermionic approach

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Cites Work

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Fermionic approach to soliton equations
Solution of soliton equations in terms of neutral fermion particles
Vertex operators and \(\tau\)-functions. Transformation groups for soliton equations. II
Vertex operators, symmetric functions, and the spin group \(\Gamma_ n\)
Generalized \(Q\)-functions and \(UC\) hierarchy of \(B\)-type
Universal characters and an extension of the KP hierarchy
Application of the Pfaffian technique to the KR and mNVN equations
Transformation groups of soliton equations. IV: A new hierarchy of soliton equations of KP-type
Transformation groups for soliton equations. Euclidean Lie algebras and reduction of the KP hierarchy
On the decomposition of tensor products of the representations of the classical groups: By means of the universal characters
Free fermions and tau-functions
Universal characters, integrable chains and the Painlevé equations
Multi-component universal character hierarchy and its polynomial tau-functions
Bilinear equations in Darboux transformations by boson-fermion correspondence
Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras
FROM KP/UC HIERARCHIES TO PAINLEVÉ EQUATIONS
On the expansion coefficients of Tau-function of the BKP hierarchy
The Adler–Shiota–van Moerbeke formula for the BKP hierarchy
Bilinear expansion of Schur functions in Schur Q-functions: A fermionic approach
The Orthogonal and Symplectic Schur Functions, Vertex Operators and Integrable Hierarchies
Generalized symplectic Schur functions and SUC hierarchy
Bilinear expansions of lattices of KP τ -functions in BKP τ -functions: A fermionic approach
Solutions of the constrained mKP hierarchy by Boson-Fermion correspondence
Modified DKP hierarchy as modified BKP hierarchy
Polynomial tau-functions of the orthogonal KP, multicomponent orthogonal KP and BUC hierarchies

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