dorsal/arxiv
View SchemaThe Complete Cohomology of $E_8$ Lie Algebra
| Authors | H. R. Karadayi, M. Gungormez |
|---|---|
| Categories | |
| ArXiv ID | physics/9701004 |
| URL | https://arxiv.org/abs/physics/9701004 |
Abstract
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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"abstract": "It is shown, for any irreducible representation of $E_8$ Lie algebra, that\neigenvalues of Casimir operators can be calculated in the form of invariant\npolinomials which are decomposed in terms of $A_8$ basis functions. The general\nmethod is applied for degrees 8,12 and 14 for which 2,8 and 19 invariant\npolinomials are obtained respectively. For each particular degree, these\ninvariant polinomials can be taken to be $E_8$ basis functions in the sense\nthat any Casimir operator of $E_8$ has always eigenvalues which can be\nexpressed as linear superpositions of them. This can be investigated by showing\nthat each one of these $E_8$ basis functions gives us a linear equation to\ncalculate weight multiplicities.",
"arxiv_id": "physics/9701004",
"authors": [
"H. R. Karadayi",
"M. Gungormez"
],
"categories": [
"math-ph",
"hep-th",
"math.MP",
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"title": "The Complete Cohomology of $E_8$ Lie Algebra",
"url": "https://arxiv.org/abs/physics/9701004"
},
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