Universal matrix Capelli identity
Mikhail Zaitsev
TL;DR
This paper introduces a universal matrix Capelli identity that unifies various Capelli identities across different algebraic structures, providing a comprehensive framework for quantum immanants.
Contribution
It presents a universal formulation of the matrix Capelli identity applicable to all quantum immanants in Reflection Equation algebra and U(gl_(M|N)).
Findings
Unified Capelli identity for quantum immanants
Derivation method for identities in Reflection Equation algebra
Application to universal enveloping algebra U(gl_(M|N))
Abstract
We propose a universal matrix Capelli identity and explain how to derive Capelli identities for all quantum immanants in the Reflection Equation algebra and in the universal enveloping algebra U(gl_(M|N)).
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Taxonomy
TopicsMatrix Theory and Algorithms