Boson mapping of the shell model algebra obtained from a seniority-dictated similarity transformation

The qualitative ideas put forward by Geyer and Lee are given quantitative content by constructing a similarity transformation which reexpresses the Dyson boson images of the single-$j$ shell fermion operators in terms of seniority bosons. It is shown that the results of Otsuka, Arima, and Iachello, or generalizations thereof which include $g$ bosons or even bosons with $J>\mathrm{}4\mathrm{}$, can be obtained in an economic and transparent way without resorting to any comparison of matrix elements.