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arXiv · 1209.1823

A Brief Note On The Definition of Signature

Hasan R. Karadayi·Meltem Gungormez
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Abstract

It is known that signature of a Weyl group element is defined in terms of the number of its simple Weyl reflections. Actual calculations hence are not always possible especially for Weyl groups with higher order like $E_8$ Weyl group. By extending the concept from signature of a Weyl reflection to signature of a weight, we show that signature of a weight is defined without referring to Weyl reflections, Though both have the same result, the signature of a weight can be calculated for any Lie algebra.

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Hasan R. Karadayi, Meltem Gungormez. 2012-09-09. A Brief Note On The Definition of Signature. https://arxiv.org/abs/1209.1823

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