Related references
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Article
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Summary: This paper focuses on the construction of the polynomial tau-functions (PTFs) for the orthogonal KP (OKP) hierarchy, multicomponent OKP hierarchy, and universal character hierarchy of B-type (BUC hierarchy). It is shown that the PTFs are zero modes of certain combinations of generating functions. The PTFs can be expressed as determinant and Pfaffian forms for the OKP and BUC hierarchies, respectively. The soliton solutions of the OKP hierarchy are also discussed.
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Summary: This paper discusses the bilinear equations of the transformed tau functions under the successive applications of the Darboux transformations for the KP hierarchy, the modified KP hierarchy, and the BKP hierarchy. New bilinear equations are derived and examples are provided.
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Summary: This paper presents the construction of quantum fields presentation and generating functions for orthogonal Schur functions and orthogonal universal characters (OUC). The boson-fermion correspondence for these two symmetric functions is discussed. Based on the quantum fields presentation, two integrable systems, namely orthogonal KP hierarchy (OKP) and OUC hierarchy, are obtained, with orthogonal Schur functions and orthogonal universal characters as their tau functions respectively. Furthermore, the (m, n)-soliton solution of the OUC hierarchy is discussed. Modified OKP and OUC hierarchies as extensions of integrable systems are also derived.
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Summary: In this paper, we investigate several topics related to the modified D-type Kadomtsev-Petviashvili (DKP) hierarchy. We first prove a conjecture that the product of the two tau functions in the modified DKP hierarchy is a tau function in the KP hierarchy. Then, we study the Darboux transformations of the DKP and modified DKP hierarchies. Finally, we provide solutions for the constrained BKP hierarchy in the fermionic representation of the infinite Lie algebra d(infinity).
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Article
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Summary: In this paper, the polynomial tau-function in terms of the universal characters of the universal character hierarchy is found, which can be treated as a zero mode of an appropriate combinatorial generating function. Furthermore, a multi-component UC hierarchy is defined and the polynomial tau-functions of the multi-component UC hierarchy are obtained.
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Article
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J. Harnad et al.
Summary: This paper presents a bilinear expansion for lattice elements of KP tau-functions labeled by partitions, showing a connection to BKP tau-functions labeled by strict partitions. The results extend previous findings on determinants and Pfaffians of skew symmetric matrices, with applications to Schur functions and Schur Q-functions. The expansion is derived using representations of KP and BKP tau-functions as vacuum expectation values of fermionic operators of charged and neutral type, respectively. The lattice structure is generated by charged creation and annihilation operators, and the result is obtained through factorization theorems for VEVs, with applications to inhomogeneous polynomial tau-functions.
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Article
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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
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