Angular Gelfand--Tzetlin Coordinates for the Supergroup UOSp(k_1/2k_2)

Abstract

We construct Gelfand--Tzetlin coordinates for the unitary orthosymplectic supergroup UOSp(k_1/2k_2). This extends a previous construction for the unitary supergroup U(k_1/k_2). We focus on the angular Gelfand--Tzetlin coordinates, i.e. our coordinates stay in the space of the supergroup. We also present a generalized Gelfand pattern for the supergroup UOSp(k_1/2k_2) and discuss various implications for representation theory