atlas::kgb::KGB Class Reference

#include <kgb.h>

Inheritance diagram for atlas::kgb::KGB:

Collaboration diagram for atlas::kgb::KGB:

Public Member Functions
	KGB (RealReductiveGroup &GR, const BitMap &Cartan_classes, bool dual_twist=false)
	~KGB ()
const TitsCoset &	basedTitsGroup () const
	The based Tits group. More...
const TitsGroup &	titsGroup () const
	The Tits group. More...
TorusPart	torus_part (KGBElt x) const
RatCoweight	base_grading_vector () const
RatCoweight	torus_factor (KGBElt x) const
TitsElt	titsElt (KGBElt x) const
size_t	torus_rank () const
Grading	base_grading () const
bool	simple_imaginary_grading (KGBElt x, RootNbr alpha) const
KGBElt	lookup (TitsElt a) const
BruhatOrder &	bruhatOrder ()
const poset::Poset &	bruhatPoset ()
virtual std::ostream &	print (std::ostream &strm, KGBElt x) const
Public Member Functions inherited from atlas::kgb::KGB_base
	KGB_base (const KGB_base &org)
virtual	~KGB_base ()
size_t	rank () const
size_t	size () const
inv_index	nr_involutions () const
const InnerClass &	innerClass () const
const RootDatum &	rootDatum () const
const WeylGroup &	weylGroup () const
const TwistedWeylGroup &	twistedWeylGroup () const
KGBElt	cross (weyl::Generator s, KGBElt x) const
KGBElt	cayley (weyl::Generator s, KGBElt x) const
KGBEltPair	inverseCayley (weyl::Generator s, KGBElt x) const
KGBElt	any_Cayley (weyl::Generator s, KGBElt x) const
KGBElt	cross (const WeylWord &ww, KGBElt x) const
KGBElt	cross (KGBElt x, const WeylWord &ww) const
unsigned int	length (KGBElt x) const
KGBElt	Hermitian_dual (KGBElt x) const
const TwistedInvolution &	nth_involution (inv_index n) const
const TwistedInvolution &	involution (KGBElt x) const
const WeightInvolution &	involution_matrix (KGBElt x) const
InvolutionNbr	inv_nr (KGBElt x) const
const DescentSet &	descent (KGBElt x) const
bool	isDescent (weyl::Generator s, KGBElt x) const
const gradings::Status &	status (KGBElt x) const
gradings::Status::Value	status (weyl::Generator s, KGBElt x) const
bool	isComplexDescent (weyl::Generator s, KGBElt x) const
bool	isDoubleCayleyImage (weyl::Generator s, KGBElt x) const
bool	isAscent (weyl::Generator s, KGBElt x) const
size_t	weylLength (KGBElt x) const
KGBEltPair	packet (KGBElt x) const
KGBEltPair	tauPacket (const TwistedInvolution &) const
size_t	packet_size (const TwistedInvolution &) const
virtual CartanNbr	Cartan_class (KGBElt x) const

Private Types
enum	State { BruhatConstructed, NumStates }

Private Member Functions
	KGB (const KGB &)
KGB &	operator= (const KGB &)
bool	is_dual_twist_stable (const RealReductiveGroup &GR, TorusPart &shift) const
void	fillBruhat ()

Private Attributes
const RealReductiveGroup &	G
std::vector< inv_index >	Cartan
	records Cartan classes of involutions More...
std::vector< TorusPart >	left_torus_part
BitSet< NumStates >	d_state
BruhatOrder *	d_bruhat
	Owned pointer to the Bruhat order on KGB (or NULL). More...
TitsCoset *	d_base
	Owned pointer to the based Tits group. More...

Additional Inherited Members
Protected Types inherited from atlas::kgb::KGB_base
typedef unsigned int	inv_index
Protected Member Functions inherited from atlas::kgb::KGB_base
	KGB_base (const InnerClass &GC, unsigned int ss_rank)
void	reserve (size_t n)
void	add_element ()
Protected Attributes inherited from atlas::kgb::KGB_base
const InnerClass &	ic
std::vector< std::vector< KGBfields > >	data
std::vector< EltInfo >	info
std::vector< InvolutionNbr >	inv_nrs
std::vector< inv_index >	inv_loc
std::vector< KGBElt >	first_of_tau
	to help find range of elements with fixed twisted involution More...

Member Enumeration Documentation

enum atlas::kgb::KGB::State

private

Enumerator
BruhatConstructed
NumStates

Constructor & Destructor Documentation

atlas::kgb::KGB::KGB ( RealReductiveGroup &  GR, const BitMap &  Cartan_classes, bool  dual_twist = false  )

explicit

atlas::kgb::KGB::~KGB

(

)

atlas::kgb::KGB::KGB ( const KGB &  )

private

Member Function Documentation

Grading atlas::kgb::KGB::base_grading ( ) const

inline

RatCoweight atlas::kgb::KGB::base_grading_vector

(

)

const

const TitsCoset& atlas::kgb::KGB::basedTitsGroup ( ) const

inline

The based Tits group.

BruhatOrder& atlas::kgb::KGB::bruhatOrder ( )

inline

const poset::Poset & atlas::kgb::KGB::bruhatPoset

(

)

void atlas::kgb::KGB::fillBruhat ( )

private

bool atlas::kgb::KGB::is_dual_twist_stable ( const RealReductiveGroup &  GR, TorusPart &  shift  ) const

private

KGBElt atlas::kgb::KGB::lookup

(

TitsElt

a

)

const

KGB& atlas::kgb::KGB::operator= ( const KGB &  )

private

std::ostream & atlas::kgb::KGB::print ( std::ostream &  strm, KGBElt  x  ) const

virtual

Reimplemented from atlas::kgb::KGB_base.

bool atlas::kgb::KGB::simple_imaginary_grading ( KGBElt  x, RootNbr  alpha  ) const

inline

TitsElt atlas::kgb::KGB::titsElt

(

KGBElt

x

)

const

const TitsGroup& atlas::kgb::KGB::titsGroup ( ) const

inline

The Tits group.

RatCoweight atlas::kgb::KGB::torus_factor

(

KGBElt

x

)

const

TorusPart atlas::kgb::KGB::torus_part ( KGBElt  x ) const

inline

size_t atlas::kgb::KGB::torus_rank

(

)

const

Member Data Documentation

std::vector<inv_index> atlas::kgb::KGB::Cartan

private

records Cartan classes of involutions

TitsCoset* atlas::kgb::KGB::d_base

private

Owned pointer to the based Tits group.

BruhatOrder* atlas::kgb::KGB::d_bruhat

private

Owned pointer to the Bruhat order on KGB (or NULL).

The class BruhatOrder contains a Poset describing the full partial order, and in addition the Hasse diagram (set of all covering relations).

BitSet<NumStates> atlas::kgb::KGB::d_state

private

const RealReductiveGroup& atlas::kgb::KGB::G

private

std::vector<TorusPart> atlas::kgb::KGB::left_torus_part

private

---

The documentation for this class was generated from the following files:

• /home/ran/atlas_project/latest_branch_07182016/sources/gkmod/kgb.h
• /home/ran/atlas_project/latest_branch_07182016/sources/gkmod/kgb.cpp