Abstract
A formula for Schur Q-functions is presented which describes the action of the Virasoro operators. For a strict partition λ= (λ1, λ2, … , λ2m) , we show that, for k≥ 1 , LkQλ=∑i=12m(λi-k)Qλ-2kϵi, where Lk is the Virasoro operator given as the quadratic form of free bosons. This main formula follows from the Plücker-like bilinear identity of Q-functions as Pfaffians: ∑i=22m(-1)i∂1Qλ1,λi∂1Qλ2,…,λi^,…,λ2m=0, where ∂1= ∂/ ∂t1. This bilinear identity must be explained in geometric words. We conjecture that the Hirota bilinear equations of the KdV hierarchy are derived from this bilinear identity.
Original language | English |
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Pages (from-to) | 1381-1389 |
Number of pages | 9 |
Journal | Letters in Mathematical Physics |
Volume | 110 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2020 Jun 1 |
Externally published | Yes |
Keywords
- Bilinear identity
- KdV hierarchy
- Q-functions
- Virasoro operators
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics