kgb.cpp File Reference

Implementation of the class KGB representing orbits of K on G/B. More...

#include "kgb.h"
#include <cassert>
#include <map>
#include <memory>
#include <set>
#include <stdexcept>
#include <iostream>
#include <iomanip>
#include <algorithm>
#include "arithmetic.h"
#include "bruhat.h"
#include "cartanclass.h"
#include "innerclass.h"
#include "lattice.h"
#include "realredgp.h"
#include "rootdata.h"
#include "subsystem.h"
#include "tits.h"
#include "weyl.h"
#include "involutions.h"
#include "basic_io.h"
#include "prettyprint.h"
#include "ioutils.h"

Include dependency graph for kgb.cpp:

Namespaces
	atlas
	atlas::kgb

Functions
KGBElt	atlas::kgb::cross (const KGB_base &kgb, KGBElt x, RootNbr alpha)
KGBElt	atlas::kgb::any_Cayley (const KGB_base &kgb, KGBElt x, RootNbr alpha)
gradings::Status::Value	atlas::kgb::status (const KGB_base &kgb, KGBElt x, RootNbr alpha)

Detailed Description

Implementation of the class KGB representing orbits of K on G/B.

This module contains code for the construction of a block in the one-sided parameter set (in other words, the subset of the one-sided parameter set corresponding to a single real form.) As explained in my Palo Alto III notes, this is equivalent to parameterizing the set K\G/B of (K,B)-orbits in G; hence the provocative title.