Manin matrices of type C: multi-parametric deformation
A. Silantyev
TL;DR
This paper introduces a multi-parametric deformation of the Brauer algebra representation linked to symplectic Lie algebras, generalizing Manin matrices of type C and analyzing their algebraic properties.
Contribution
It develops a multi-parametric deformation framework for Manin matrices of type C using quadratic algebra representations.
Findings
Derived pairing operators for quadratic algebras
Calculated ranks of pairing operators
Determined dimensions of quadratic algebra components
Abstract
We constructed a multi-parametric deformation of the Brauer algebra representation related with the symplectic Lie algebras. The notion of Manin matrix of type C was generalised to the case of the multi-parametric deformation by using this representation and corresponding quadratic algebras. We derived pairing operators for these quadratic algebras and minors for the considered Manin matrices. The rank of pairing operators and dimensions of components of quadratic algebras were calculated.
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