The Complete Cohomology of $E_8$ Lie Algebra

Details The Complete Cohomology of $E_8$ Lie Algebra The Complete Cohomology of $E_8$ Lie Algebra

1997-01-07

arxiv.org/abs/physics/9701004v2

Physics

Mathematical Physics

17 pages, in TeX file, change in e-mail address

Scientific paper

It is shown, for any irreducible representation of $E_8$ Lie algebra, that eigenvalues of Casimir operators can be calculated in the form of invariant polinomials which are decomposed in terms of $A_8$ basis functions. The general method is applied for degrees 8,12 and 14 for which 2,8 and 19 invariant polinomials are obtained respectively. For each particular degree, these invariant polinomials can be taken to be $E_8$ basis functions in the sense that any Casimir operator of $E_8$ has always eigenvalues which can be expressed as linear superpositions of them. This can be investigated by showing that each one of these $E_8$ basis functions gives us a linear equation to calculate weight multiplicities.

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