Polynomial tau-functions of the KP, BKP, and the <i>s</i>-component KP hierarchies
Victor G. Kač, Natasha Rozhkovskaya, Johan van de Leur
Abstract
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 with partitions in s parts.
Topics & Concepts
MathematicsComponent (thermodynamics)PolynomialPure mathematicsHierarchyFunction (biology)Algebra over a fieldZero (linguistics)Symmetric polynomialGenerating functionCombinatoricsMatrix polynomialMathematical analysisPhysicsBiologyPhilosophyMarket economyEvolutionary biologyThermodynamicsEconomicsLinguisticsAdvanced Combinatorial MathematicsAlgebraic structures and combinatorial modelsMolecular spectroscopy and chirality