atlas::tits Namespace Reference

Classes
class	atlas::tits::TitsElt
	Represents an element of a Tits group. More...
class	atlas::tits::TitsGroup
	Represents a finite subgroup of the normalizer in $G$ of the Cartan $H$. More...
struct	atlas::tits::TE_Entry
Typedefs
typedef latticetypes::SmallBitVector	TorusPart
	Element of (Z/2Z)^rank, representing an element of T(2).
typedef std::vector< TitsElt >	TitsEltList
Functions
weyl::Twist	makeTwist (const latticetypes::LatticeMatrix &d, const rootdata::RootDatum &rd)

---

Typedef Documentation

typedef std::vector<TitsElt> atlas::tits::TitsEltList

Definition at line 31 of file tits_fwd.h.

typedef latticetypes::SmallBitVector atlas::tits::TorusPart

Element of (Z/2Z)^rank, representing an element of T(2). The cocharacter lattice X_*(T) of T is always represented by Z^rank; the map X_*(T)-> T given by lambda^vee exp(pi i lambda^vee) has 2X_*(T) as kernel, and induces a bijection of X_*(T)/2X_*(T) with the group T(2) of elements of order 2; hence T(2) is represented by (Z/2Z)^rank Definition at line 41 of file tits.h. Referenced by atlas::kgb::KGBHelp::backtrack_seed(), atlas::kgb::KGBHelp::grading_seed(), atlas::kgb::KGBHelp::is_compact(), atlas::tits::TitsGroup::left_add(), atlas::tits::TitsGroup::left_torus_part(), atlas::kgb::KGBHelp::naive_seed(), atlas::tits::TitsGroup::pull_across(), atlas::tits::TitsGroup::push_across(), atlas::tits::TitsGroup::reflect(), atlas::tits::TitsGroup::right_add(), atlas::tits::TitsGroup::right_torus_part(), atlas::tits::TitsGroup::simpleCoroot(), atlas::tits::TitsGroup::simpleRoot(), atlas::tits::TitsElt::t(), and atlas::tits::TitsElt::TitsElt().

---

Function Documentation

weyl::Twist atlas::tits::makeTwist (  const latticetypes::LatticeMatrix &  d, const rootdata::RootDatum &  rd )

Synopsis: Returns the twist defined by |d|. Precondition: |d| holds an involution of the root datum which fixes the positive Weyl chamber. The value computed essentially gives the functionality of WeylGroup::twist and of TitsGroup::twist, but it cannot use those methods since it is called before they are available: our task here is to prepare the data that will be used by those methods. Definition at line 201 of file tits.cpp. References atlas::matrix::Matrix< C >::apply(), atlas::rootdata::RootDatum::beginSimpleRoot(), atlas::rootdata::RootDatum::endSimpleRoot(), atlas::setutils::find_index(), atlas::latticetypes::LatticeMatrix, atlas::rootdata::RootDatum::rank(), and atlas::weyl::Twist. Referenced by atlas::tits::TitsGroup::TitsGroup().

---