Extensions of the tensor algebra and their applications

Details Extensions of the tensor algebra and their applications Extensions of the tensor algebra and their applications

2009-09-30

arxiv.org/abs/0909.5586v4

Mathematics

Representation Theory

43 pages; some expositions improved; to appear in Comm. Algebra

Scientific paper

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).

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