matrix* Weyl_root_orbit(entry* v)
{ lie_Index i,j,r=Lierank(grp),s=Ssrank(grp);
entry* x=mkintarray(r); matrix* orbit, *result; entry** m;
lie_Index dc=Detcartan();
mulvecmatelm(v,Cartan()->elm,x,s,r);
orbit=Weyl_orbit(x,NULL);
result=mkmatrix(orbit->nrows,s); m=result->elm;
mulmatmatelm(orbit->elm,Icartan()->elm,m,orbit->nrows,s,s);
freemem(orbit);
for (i=0; i<result->nrows; ++i)
for (j=0; j<s; ++j) m[i][j]/=dc;
return result;
}
matrix* Icartan(void)
{ if (simpgroup(grp)) return simp_icart(Liecomp(grp,0));
{ matrix* result=mat_null(Lierank(grp),Ssrank(grp)); entry** m=result->elm;
_index k,t=0;
entry det=Detcartan(); /* product of determinants of simple factors */
for (k=0; k<grp->g.ncomp; ++k)
{ simpgrp* g=Liecomp(grp,k);
_index i,j,r=g->lierank;
entry** a=simp_icart(g)->elm;
entry f=det/simp_detcart(g); /* multiplication factor */
for (i=0; i<r; ++i) for (j=0; j<r; ++j) m[t+i][t+j]=f*a[i][j];
t+=r;
}
return result;
}
}
