Sklyanin Determinant for Reflection Algebra

Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of the reflection algebra. We give a combinatorial description of Sklyanin determinant suitable for explicit computations

Vertex operators arising from Jacobi-Trudi identities

We give an interpretation of the boson-fermion correspondence as a direct consequence of Jacobi-Trudi identity. This viewpoint enables us to construct from a generalized version of the Jacobi-Trudi identity the action of Clifford algebra on polynomial algebras that arrives as analogues of the algebra of symmetric functions. A generalized Giambelli identity is also proved to follow from that identity. As applications, we obtain explicit formulas for vertex operators corresponding to characters of the classical Lie algebras, shifted Schur functions, and generalized Schur symmetric functions associated to linear recurrence relations.Comment: 23 page

Polynomial Tau-functions of the KP, BKP, and the s-Component KP Hierarchies

We show that any polynomial tau-function of the s-component KP and the BKP hierarchies can be interpreted as a zero mode of an appropriate combinatorial generating function. As an application, we obtain explicit formulas for all polynomial tau-functions of these hierarchies in terms of Schur polynomials and Q-Schur polynomials respectively. We also obtain formulas for polynomial tau-functions of the reductions of the s-component KP hierarchy associated to partitions in s parts.Comment: 28 page