atlas::rootdata Namespace Reference

Classes
class	RootDatum
	Based root datum for a complex reductive group. More...
class	RootSystem
class	weight_compare

Typedefs
typedef int_Vector	Root
typedef WeightList::const_iterator	WRootIterator

Functions
RatWeight	rho (const RootDatum &rd)
RatCoweight	rho_check (const RootDatum &rd)
CoweightInvolution	dualBasedInvolution (const WeightInvolution &q, const RootDatum &rd)
RootNbrSet	makeOrthogonal (const RootNbrSet &o, const RootNbrSet &subsys, const RootSystem &rs)
	Returns the elements of |subsys| which are orthogonal to all elements of |o|. More...
void	toDistinguished (WeightInvolution &q, const RootDatum &rd)
	Transforms q, assumed a root datum involution, into a based root datum involution w.q, which fixes the positive Weyl chamber. More...
WeylWord	wrt_distinguished (const RootSystem &rs, RootNbrList &Delta)
void	make_positive (const RootSystem &rs, RootNbr &alpha)
WeylWord	conjugate_to_simple (const RootSystem &rs, RootNbr &alpha)
WeightInvolution	refl_prod (const RootNbrSet &rset, const RootDatum &rd)
RootDatum	integrality_datum (const RootDatum &rd, const RatWeight &gamma)
unsigned int	integrality_rank (const RootDatum &rd, const RatWeight &gamma)
RationalList	integrality_points (const RootDatum &rd, const RatWeight &gamma)

Typedef Documentation

typedef int_Vector atlas::rootdata::Root

typedef WeightList::const_iterator atlas::rootdata::WRootIterator

Function Documentation

WeylWord atlas::rootdata::conjugate_to_simple	(	const RootSystem &	rs,
		RootNbr &	alpha
	)

CoweightInvolution atlas::rootdata::dualBasedInvolution	(	const WeightInvolution &	q,
		const RootDatum &	rd
	)

RootDatum atlas::rootdata::integrality_datum	(	const RootDatum &	rd,
		const RatWeight &	gamma
	)

RationalList atlas::rootdata::integrality_points	(	const RootDatum &	rd,
		const RatWeight &	gamma
	)

unsigned int atlas::rootdata::integrality_rank	(	const RootDatum &	rd,
		const RatWeight &	gamma
	)

void atlas::rootdata::make_positive	(	const RootSystem &	rs,
		RootNbr &	alpha
	)

RootNbrSet atlas::rootdata::makeOrthogonal	(	const RootNbrSet &	o,
		const RootNbrSet &	subsys,
		const RootSystem &	rs
	)

Returns the elements of |subsys| which are orthogonal to all elements of |o|.

WeightInvolution atlas::rootdata::refl_prod	(	const RootNbrSet &	rset,
		const RootDatum &	rd
	)

RatWeight atlas::rootdata::rho

(

const RootDatum &

rd

)

RatCoweight atlas::rootdata::rho_check

(

const RootDatum &

rd

)

void atlas::rootdata::toDistinguished	(	WeightInvolution &	q,
		const RootDatum &	rd
	)

Transforms q, assumed a root datum involution, into a based root datum involution w.q, which fixes the positive Weyl chamber.

Note that wq is then automatically an involution permuting the simple roots

WeylWord atlas::rootdata::wrt_distinguished	(	const RootSystem &	rs,
		RootNbrList &	Delta
	)