116 lines
3.2 KiB

#ifndef WEYL_H
#define WEYL_H
#include <inttypes.h>
struct _simple_type;
struct _semisimple_type;
struct _weylgroup_element;
struct _weylgroup;
struct _doublecoset;
struct _doublecoset_list;
struct _doublequotient;
typedef uint64_t weylid_t;
typedef struct _simple_type simple_type_t;
typedef struct _semisimple_type semisimple_type_t;
typedef struct _weylgroup_element weylgroup_element_t;
typedef struct _weylgroup weylgroup_t;
typedef struct _doublecoset doublecoset_t;
typedef struct _doublecoset_list doublecoset_list_t;
typedef struct _doublequotient doublequotient_t;
/***************************** structures *******************************/
struct _simple_type {
char series;
int rank;
struct _semisimple_type {
int n;
simple_type_t *factors;
struct _weylgroup_element {
int *word;
int wordlength;
weylgroup_element_t **left;
weylgroup_element_t **right;
weylgroup_element_t *opposite;
int is_root_reflection; // boolean value
weylid_t id; // a unique id
int index;
// only set if quotient is generated
doublecoset_t *coset;
struct _weylgroup {
semisimple_type_t type;
weylgroup_element_t *elements;
weylgroup_element_t **lists;
int *letters;
struct _doublecoset {
doublecoset_list_t *bruhat_lower;
doublecoset_list_t *bruhat_higher;
doublecoset_t *opposite;
weylgroup_element_t *max;
weylgroup_element_t *min;
int index;
struct _doublecoset_list {
doublecoset_t *to;
doublecoset_list_t *next;
struct _doublequotient {
semisimple_type_t type;
int left_invariance; // bitmask with rank bits
int right_invariance;
int count; // number of double cosets
doublecoset_t *cosets;
weylgroup_element_t *group;
doublecoset_list_t *lists; // only for memory allocation / freeing
weylgroup_element_t **grouplists; // only for memory allocation / freeing
int *groupletters; // only for memory allocation / freeing
/***************************** functions **************************************/
/* query some basic information on root systems / Weyl groups */
// the rank
int weyl_rank(semisimple_type_t type);
// the order of the weyl group
int weyl_order(semisimple_type_t type);
// the number of reduced positive roots
int weyl_positive(semisimple_type_t type);
// the Cartan matrix (has rank columns and rank rows)
void weyl_cartan_matrix(semisimple_type_t type, int *m);
// the opposition involution as a map from simple roots to simple roots (indexed from 0 to rank-1)
int weyl_opposition(semisimple_type_t type, int simple_root);
/* generate the Weyl group:
weyl_destroy() has to be used to free memory
weylgroup_t *weyl_generate(semisimple_type_t type);
void weyl_destroy(weylgroup_t *group);
/* generate a double quotient of the Weyl group and its Bruhat order:
left_invariance and right_invariance are bitmaps specifying a subset of the simple roots
The Weyl group will be quotiented from the left and right by the subgroups generated by these simple root reflections
weyl_destroy_bruhat() has to be used to free memory
doublequotient_t *weyl_generate_bruhat(semisimple_type_t type, int left_invariance, int right_invariance);
void weyl_destroy_bruhat(doublequotient_t *dq);