Orthogonal Gelfand-Zetlin algebras. I (Q1567459)

The author defines a class of associative algebras which have properties similar to those of the enveloping algebra of \(\mathfrak{gl}(n,\mathbb{C})\). They also share several features of the representation theory. As particular examples the author gives: the enveloping algebra of \(\mathfrak{gl}(n,\mathbb{C})\), polynomial algebras and extended Heisenberg algebras. In some restricted cases the representation theory is similar to the one developed by \textit{S. P. Smith} [Trans. Am. Math. Soc. 322, 285-314 (1990; Zbl 0732.16019)].