# dualCoxeterNumber -- returns the dual Coxeter number of a simple Lie algebra

## Synopsis

• Usage:
dualCoxeterNumber(g)
• Inputs:
• g, an instance of the type LieAlgebra, a simple Lie algebra
• Outputs:
• n, an integer, the dual Coxeter number of g

## Description

The dual Coxeter number is defined as the sum of the comarks plus 1. See Di Francesco, Mathieu, and Senechal, Conformal Field Theory, Springer Graduate Texts in Theoretical Physics, Formula (13.35) and Appendix A.

 i1 : dualCoxeterNumber("A",2) o1 = 3 i2 : g=simpleLieAlgebra("A",2) o2 = g o2 : LieAlgebra i3 : dualCoxeterNumber(g) o3 = 3

## Ways to use dualCoxeterNumber :

• "dualCoxeterNumber(LieAlgebra)"
• "dualCoxeterNumber(String,ZZ)"

## For the programmer

The object dualCoxeterNumber is .