2009/09/30 by Minoru Itoh, Itoh, Minoru
Mathematics · Physics and Astronomy · #15A15 #15A72 #17B35 #20C30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.0909.5586
openalex publication_date 2009/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article presents a natural extension of the tensor algebra. In addition to "left multiplications" by vectors, we can consider "derivations" by covectors as basic operators on this extended algebra. These two types of operators satisfy an analogue of the canonical commutation relations. This algebra and these operators have some applications: (i) applications to invariant theory related to tensor products, and (ii) applications to immanants. The latter one includes a new method to study the quantum immanants in the universal enveloping algebras of the general linear Lie algebras and their Capelli type identities (the higher Capelli identities).