Angular Gelfand--Tzetlin Coordinates for the Supergroup UOSp(k_1/2k_2)
Thomas Guhr, Heiner Kohler
TL;DR
This paper develops angular Gelfand--Tzetlin coordinates for the supergroup UOSp(k_1/2k_2), extending previous work on the unitary supergroup, with implications for representation theory.
Contribution
It introduces a new construction of Gelfand--Tzetlin coordinates for the supergroup UOSp(k_1/2k_2), expanding the mathematical framework for supergroup analysis.
Findings
Constructed angular Gelfand--Tzetlin coordinates for UOSp supergroup
Presented a generalized Gelfand pattern for UOSp
Discussed implications for supergroup representation theory
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.
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