On the imaginary simple roots of the Borcherds algebra g-II(9,1)
May, 199710 pages
Published in:
- Nucl.Phys.B 510 (1998) 721-738
e-Print:
- hep-th/9705144 [hep-th]
Report number:
- IASSNS-HEP-97-53,
- AEI-037
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Abstract:
In a recent paper (hep-th/9703084) it was conjectured that the imaginary simple roots of the Borcherds algebra at level 1 are its only ones. We here propose an independent test of this conjecture, establishing its validity for all roots of norm . However, the conjecture fails for roots of norm -10 and beyond, as we show by computing the simple multiplicities down to norm -24, which turn out to be remakably small in comparison with the corresponding multiplicities. Our derivation is based on a modified denominator formula combining the denominator formulas for and , and provides an efficient method for determining the imaginary simple roots. In addition, we compute the multiplicities of all roots up to height 231, including levels up to and norms -42.- 11.25.H
- 02.10.S
- Hyperbolic Kac-Moody algebras
- String vertex operators
- algebra: Kac-Moody
- algebra: E(10)
- algebra: representation
- analytic properties
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