Essentially typical representations of Lie superalgebras \({\mathfrak gl}(n| m)\) in the Gel'fand-Tsetlin basis (Q919454)

The paper is devoted to a special class of finite-dimensional irreducible modules with respect to the Lie superalgebra \({\mathfrak gl}(n| m)\). Such a typical module W(n,m) is said to be essentially typical, if there exists no flag of submodules W(n,m)\(\supset...\supset W(n,p)\supset...\supset W(n,1)\) with at least one irreducible \({\mathfrak gl}(n| p)\)-submodule W(n,p). The author modifies the concept of the Gel'fand-Tsetlin basis to the case of essentially typical \({\mathfrak gl}(n| m)\)-module and deduces an explicit formula for the action of \({\mathfrak gl}(n| m)\) in such a basis.