11 research outputs found
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