Vertex operators, t-boson model and weighted plane partitions in finite boxes

摘要

We consider two different subjects: the algebra of Hall-Littlewood functions and t-boson model. Tsilevich and Sulkowski, respectively, give that the creation operator B(u) in the monodromy matrix of t-boson model can be represented by H(z), where H(z) and H-perpendicular to (z) are vertex operators closely related to the Hall-Littlewood functions. In this paper, we obtain that the annihilation operator C(u) in the monodromy matrix and other relations of t-boson model can also be realized in the algebra of Hall-Littlewood functions. Meanwhile, we get that the generating functions of weighted plane partitions in finite boxes can be obtained from the operators B(u), C(u).