Algebras are objects which reveal symmetries of the physical world and strengthen understanding of physics, chemistry, quantum information, biology, and their mathematical connections. These symmetries are organized via a mathematical framework called representation theory. Finite-dimensional representation theory involves the realization of an algebra as arrays of numbers (matrices); infinite-dimensional representation theory involves the realization of an algebra as functions, including differentiation from calculus. This project focuses on the infinite-dimensional representations of superalgebras as motivated by supersymmetry of particle physics. The Principal Investigator (PI) expects three main results from the project: (1) creation of new infinite-dimensional super representations; (2) simplification of super representations into their constituent parts; and, (3) determination of formulas to allow for computation and increased applicability of representation theory to scientific phenomena. The award also supports undergraduate research trainees and a doctoral student supervised by the PI in solving one or more of the research problems of the project. In more detail, the project has three main technical parts. The first part is that the PI will establish superalgebra homomorphisms from the universal enveloping algebra of orthosymplectic Lie superalgebras to tensor products of Clifford-Weyl superalgebras. The second part relies on the PI building upon previous coll