weyl_character_formula.at Function References¶

find_ratvec_mod_vec¶

find_ratvec_mod_vec:[ratvec] v, ratvec w->int Defined in line number 33.

reduce_ratvecs_mod_lattice¶

reduce_ratvecs_mod_lattice:[ratvec] S->[ratvec] Defined in line number 37.

W_orbit_torus_element¶

W_orbit_torus_element:RootDatum rd,ratvec v->[ratvec] Defined in line number 44.

centralizer¶

centralizer:RootDatum rd,ratvec v->RootDatum Defined in line number 50.

QmodZ_order¶

QmodZ_order:ratvec v->int Defined in line number 56.

Order of element of Q/Z

eval_char_T¶

eval_char_T:vec lambda, ratvec v,cyclotomicField F->cyclotomicFieldElement Defined in line number 60.

weyl_denominator_quotient¶

weyl_denominator_quotient:RootDatum rd, ratvec v,cyclotomicField F->cyclotomicFieldElement Defined in line number 64.

Product of $$1-\exp(-alpha)(t)$$ over all posroots $$\alpha$$ making it nonzero

wcf_semisimple_simply_connected¶

wcf_semisimple_simply_connected:RootDatum rd, vec lambda,ratvec v,cyclotomicField F->cyclotomicFieldElement Defined in line number 75.

Weyl character formula for finite dimensional with extremal weight lambda at t=exp_1(v), in the semisimple simply connected case

wcf¶

wcf:RootDatum rd, vec lambda, ratvec t, cyclotomicField F->cyclotomicFieldElement Defined in line number 100.

Weyl character formula for finite dimensional with extremal weight lambda exp_1(v)

wcf_long¶

wcf_long:RootDatum rd, vec lambda,ratvec v,cyclotomicField F->(cyclotomicFieldElement,[cyclotomicFieldElement]) Defined in line number 110.

wcf¶

wcf:RootDatum rd, vec lambda,ratvec v->cyclotomicFieldElement Defined in line number 133.

wcf¶

wcf:vec lambda,(RootDatum rd,ratvec v)->cyclotomicFieldElement Defined in line number 135.

wcf¶

wcf:Param p, ratvec v->cyclotomicFieldElement Defined in line number 137.

wcf_long¶

wcf_long:RootDatum rd, vec lambda,ratvec v->(cyclotomicFieldElement,[cyclotomicFieldElement]) Defined in line number 140.

wcf_long¶

wcf_long:vec lambda,(RootDatum rd,ratvec v)->(cyclotomicFieldElement,[cyclotomicFieldElement]) Defined in line number 143.

wcf_strong_real¶

wcf_strong_real:RootDatum rd, ratvec lambda,ratvec v->(rat,rat) Defined in line number 161.

Weyl character formula for highest weight lambda evaluated on an element x in T with x^2 in Z

wcf_strong_real¶

wcf_strong_real:Param p,ratvec v->(rat,rat) Defined in line number 179.

Weyl character formula for finite dimensional p evaluated on an element x in T with x^2 in Z

wcf¶

wcf:[vec] weights,ratvec v->cyclotomicFieldElement Defined in line number 185.

Evaluate sum of weights at t

torus_factor_x¶

torus_factor_x:RealForm G->(RootDatum,ratvec) Defined in line number 194.

Torus factor of strong real form of x

wcf_report¶

wcf_report:RealForm G, vec lambda, ratvec t->void Defined in line number 198.

Output of Weyl character formula

wcf_report¶

wcf_report:Param p,ratvec t->void Defined in line number 203.

wcf_report¶

wcf_report:RealForm G, int height_bound, ratvec t->void Defined in line number 207.

Run over all finite dimensionals up to height bound