Superintegrability in $$\beta $$-deformed Gaussian Hermitian matrix model from W-operators
V. Mishnyakov, A. Oreshina
Abstract
Abstract This paper is devoted to the phenomenon of superintegrability. This phenomenon is manifested in the existence of a formula for character averages, expressed through the same characters at special points and of its various generalization. In this paper we develop a method of proving such formulas from first principle from Virasoro constraints and W -representation. We apply it to prove the formula for the Jack functions averages – appropriate analogue of characters for the $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> -deformed Hermitian Gaussian matrix model. We also sketch the construction of W -operators from Calogero–Ruijsenaars Hamiltonians.
Topics & Concepts
Hermitian matrixGeneralizationMathematicsCharacter (mathematics)Matrix (chemical analysis)GaussianSketchPure mathematicsRepresentation (politics)BETA (programming language)Operator (biology)Mathematical physicsMathematical analysisPhysicsQuantum mechanicsGeometryComputer scienceAlgorithmRepressorComposite materialTranscription factorProgramming languageMaterials scienceGeneLawPolitical scienceBiochemistryChemistryPoliticsAlgebraic structures and combinatorial modelsAdvanced Algebra and GeometryQuantum Mechanics and Non-Hermitian Physics