Abstract
In a previous paper we constructed all polynomial tau-functions of the 1-component KP hierarchy, namely, we showed that any such tau-function is obtained from a Schur polynomial s_λ(t)
by certain shifts of arguments. In the present paper we give a simpler proof of this result, using the (1-component) boson–fermion correspondence. Moreover, we show that this approach can be applied to the s-component KP hierarchy, using the
s-component boson–fermion correspondence, finding thereby all its polynomial tau-functions. We also find all polynomial tau-functions for the reduction of the
s-component KP hierarchy, associated to any partition consisting of
s positive parts.
by certain shifts of arguments. In the present paper we give a simpler proof of this result, using the (1-component) boson–fermion correspondence. Moreover, we show that this approach can be applied to the s-component KP hierarchy, using the
s-component boson–fermion correspondence, finding thereby all its polynomial tau-functions. We also find all polynomial tau-functions for the reduction of the
s-component KP hierarchy, associated to any partition consisting of
s positive parts.
| Original language | English |
|---|---|
| Pages (from-to) | 1-19 |
| Number of pages | 19 |
| Journal | Publications of the Research Institute for Mathematical Sciences |
| Volume | 58 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 17 Feb 2022 |
Keywords
- KP hierarchy
- multicomponent
- KP
- tau-functions
- Schur polynomials