atlas::kgb Namespace Reference

Classes
class	atlas::kgb::FiberData
	A |FiberData| object associates to each twisted involution a subspace describing how corresponding Tits elements should be normalized. More...
class	atlas::kgb::KGBHelp
class	atlas::kgb::InvolutionCompare
class	atlas::kgb::IndexCompare
struct	atlas::kgb::KGBInfo
class	atlas::kgb::KGB
	Represents the orbits of K on G/B for a particular real form. More...
Typedefs
typedef size_t	KGBElt
typedef std::vector< KGBElt >	KGBEltList
typedef std::pair< KGBElt, KGBElt >	KGBEltPair
typedef std::vector< KGBEltPair >	KGBEltPairList
typedef bitset::RankFlags	Descent
typedef std::vector< Descent >	DescentList
Functions
gradings::Grading	square_class_grading_offset (const complexredgp::ComplexReductiveGroup &G, cartanclass::square_class csc)
gradings::Grading	grading_offset_for (const realredgp::RealReductiveGroup &GR)
void	makeHasse (std::vector< set::SetEltList > &, const KGB &)
gradings::Grading	grading_offset_for (const realredgp::RealReductiveGroup &G)
	Returns the grading offset (on simple roots) adapted to |G|. This flags the simple roots that are noncompact imaginary at the fundamental Cartan in G.
gradings::Grading	square_class_grading_offset (const complexredgp::ComplexReductiveGroup &G, cartanclass::square_class csc)
	Returns the grading offset for the base real form of |csc|.
void	makeHasse (std::vector< set::SetEltList > &hd, const KGB &kgb)
	Puts in hd the hasse diagram data for the Bruhat ordering on KGB.
Variables
const KGBElt	UndefKGB = ~0ul

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Typedef Documentation

typedef bitset::RankFlags atlas::kgb::Descent

Definition at line 33 of file kgb_fwd.h. Referenced by atlas::kgb::KGB::descent(), and makeHasse().

typedef std::vector<Descent> atlas::kgb::DescentList

Definition at line 34 of file kgb_fwd.h.

typedef size_t atlas::kgb::KGBElt

Definition at line 27 of file kgb_fwd.h. Referenced by atlas::kgb::KGB::cayley(), atlas::kgb::KGBHelp::cayleyExtend(), atlas::kgb::KGB::cross(), atlas::kgb::KGBHelp::cross_extend(), atlas::kgb::KGBHelp::export_tables(), atlas::kgb::KGBHelp::fill(), atlas::kgb::KGB::KGB(), atlas::kgb::KGBHelp::KGBHelp(), and makeHasse().

typedef std::vector<KGBElt> atlas::kgb::KGBEltList

Definition at line 28 of file kgb_fwd.h.

typedef std::pair<KGBElt,KGBElt> atlas::kgb::KGBEltPair

Definition at line 30 of file kgb_fwd.h. Referenced by atlas::kgb::KGB::inverseCayley(), atlas::kgb::KGB::KGB(), makeHasse(), and atlas::kgb::KGB::tauPacket().

typedef std::vector<KGBEltPair> atlas::kgb::KGBEltPairList

Definition at line 31 of file kgb_fwd.h. Referenced by atlas::kgb::KGB::KGB().

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Function Documentation

gradings::Grading grading_offset_for (  const realredgp::RealReductiveGroup &  G  )  [static]

Returns the grading offset (on simple roots) adapted to |G|. This flags the simple roots that are noncompact imaginary at the fundamental Cartan in G. Algorithm: the variable |rset| is first made to flag, among the imaginary roots of the fundamental Cartan, those that are noncompact for the chosen representative (in the adjoint fiber) of the real form of |G|. The result is formed by extracting only the information concerning the presence of the {simple} roots in |rset|. Definition at line 1266 of file kgb.cpp. References atlas::gradings::Grading, atlas::realredgp::RealReductiveGroup::noncompactRoots(), atlas::cartanclass::restrictGrading(), atlas::realredgp::RealReductiveGroup::rootDatum(), atlas::rootdata::RootSet, and atlas::rootdata::RootDatum::simpleRootList().

gradings::Grading grading_offset_for (  const realredgp::RealReductiveGroup &  GR  )  [static]

Referenced by atlas::kgb::KGBHelp::KGBHelp().

void makeHasse (  std::vector< set::SetEltList > &  hd, const KGB &  kgb )  [static]

Puts in hd the hasse diagram data for the Bruhat ordering on KGB. Explanation: this is the closure ordering of orbits. We use the algorithm from Richardson and Springer. Definition at line 1289 of file kgb.cpp. References atlas::kgb::KGB::cayley(), atlas::kgb::KGB::cross(), atlas::kgb::KGB::descent(), Descent, atlas::bitset::BitSet< n >::firstBit(), atlas::kgb::KGB::inverseCayley(), atlas::kgb::KGB::isAscent(), KGBElt, KGBEltPair, atlas::bitset::BitSet< n >::none(), atlas::kgb::KGB::size(), and atlas::kgb::KGB::status().

void makeHasse (  std::vector< set::SetEltList > &  , const KGB &  )  [static]

Referenced by atlas::kgb::KGB::fillBruhat().

gradings::Grading square_class_grading_offset (  const complexredgp::ComplexReductiveGroup &  G, cartanclass::square_class  csc )  [static]

Returns the grading offset for the base real form of |csc|. Precondition: |csc| specifies a square class (coset in adjoint fiber group) Definition at line 1280 of file kgb.cpp. References atlas::cartanclass::Fiber::class_base(), atlas::complexredgp::ComplexReductiveGroup::fundamental(), atlas::cartanclass::Fiber::noncompactRoots(), atlas::cartanclass::restrictGrading(), atlas::complexredgp::ComplexReductiveGroup::rootDatum(), atlas::rootdata::RootSet, and atlas::rootdata::RootDatum::simpleRootList().

gradings::Grading square_class_grading_offset (  const complexredgp::ComplexReductiveGroup &  G, cartanclass::square_class  csc )  [static]

Referenced by atlas::kgb::KGBHelp::KGBHelp().

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Variable Documentation

const KGBElt atlas::kgb::UndefKGB = ~0ul

Definition at line 36 of file kgb.h. Referenced by atlas::kgb::KGBHelp::export_tables(), atlas::kgb::KGB::KGB(), and atlas::kgb::KGBHelp::KGBHelp().

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