Supersymmetric Schur Q-functions and super BKP hierarchy. (English) Zbl 1506.05210
Summary: In this paper, we first define supersymmetric Schur Q-functions and give their vertex operators realization. By means of the vertex operator, we obtain a series of non-linear partial differential equations of infinite order, called the super BKP hierarchy and the super BKP hierarchy governs the supersymmetric Schur Q-functions as the tau functions. Moreover, we prove that supersymmetric Schur Q-functions can be viewed as compound Schur Q-functions. This means that we can study the properties of supersymmetric Schur Q-functions according to Schur Q-functions, such as their applications in representation theory.
MSC:
| 05E05 | Symmetric functions and generalizations |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 17B69 | Vertex operators; vertex operator algebras and related structures |
| 37K06 | General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
supersymmetric Schur Q-functions; vertex operators; super BKP hierarchy; compound Schur Q-functionsReferences:
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