Physical Sciences and Mathematics Commons^™

Decomposing Vector Space Representations Of The Lie Algebras S[2c And S[2r, Brian W. Gleason

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

It is known that any finite-dimensional representation of a semi-simple Lie algebra is decomposable into a direct sum of irreducible representations. Here we prove some theoretical results that allow us to construct an efficient algorithm for computing such a decomposition for representations of s[2C and s[2R. We then implement this algorithm in a procedure for the computer algebra system Maple that will quickly and easily perform the decomposition. We also give several examples of this decomposition performed by the procedure in order to illustrate its advantages over calculations done ‘by hand'.