Abstract
The Gaussian matrix model is known to deform to the q,t-matrix model. We consider further deformation to the elliptic q,t matrix model by properly deforming the Gaussian density as well as the Vandermonde factor. Properties of an associated basis of symmetric functions that provide the matrix model property <char>∼char in the deformed elliptic case are discussed.
Highlights
Eigenvalue matrix models are associated with many different issues in modern string theory
The logarithmic models attract a lot of attention these days, because they are associated with both the AGT correspondence [1] and with CFT/Painleve correspondence [2], where one applies peculiar techniques based on various Selberg and Kadell type formulas [3], while, in the case of ordinary time-variables, one has direct relation to KP/Toda integrability and Virasoro-like constraints, which get obscure after reduction to a few Miwa variables
Matrix models in Miwa variables are associated with the Jack polynomials [3], or their generalized versions [5]
Summary
Eigenvalue matrix models are associated with many different issues in modern string theory. In the particular case of the ordinary N × N Gaussian Hermitian model, this symmetric function is an SL(N ) character, the Schur polynomial. An immediate deformation of the Gaussian Hermitian model to the q, t matrix model was recently presented in [11] This does not come as a surprise that the set of symmetric polynomials associated with such deformation turns out to be Macdonald polynomials. Such an approach proved to be a very powerful tool to. The naive Hamiltonians proposed in [14, 15] have distinct eigenfunctions (see [16, sec.6.3]) It is still an open question if these two systems of functions can be related by a unitary transform.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
