Script Reference
modules.at
Operations on standard and irreducible modules: tagged parameters, composition series, and character formulas.
Mathematical background
Provides a uniform interface for working with standard modules \(I(p)\) and their irreducible quotients \(J(p)\), together with functions for computing composition series and Kazhdan–Lusztig characters.
Definitions
| Name | Signature | Description |
|---|---|---|
| I | (Param p) = tag_Param: | |
| J | p)=tag_Param: | |
| to_str | (Param p) = string: | |
| to_str_std | (Param p) = string: "I"+to_str(p) | |
| to_str_irr | (Param p) = string: "J"+to_str(p) | |
| to_str_K_types | p) = string: | |
| to_str | (tag_Param(p,type)) = string: | |
| to_str | (ParamPol P) = [string]: | |
| to_str | (ParamPol P,string type) = [string]: | |
| array_prints | ([string] A) = void: { print strings, one per line } | print strings, one per line |
| composition_series | (Param p,string type) = tag_ParamPol: | |
| composition_series | (tag_ParamPol(P,type))= tag_ParamPol: | |
| character_formula | (tag_Param(p,type)) = tag_ParamPol: | |
| character_formula | (tag_ParamPol(P,type)) = tag_ParamPol: | |
| show | (ParamPol P) = void: array_prints(to_str(P)) | |
| show | (tag_ParamPol(,type):tP) = void: | |
| show | tP) = void: prints(to_str(tP)) | |
| show | x,ratvec lambda) = void: | |
| as_pol | (tag_Param(p,type)) = tag_ParamPol: | |
| = | (tag_Param(p,type_p),tag_Param(q,type_q)) = bool: | |
| character | (tag_ParamPol (P,type)) = ParamPol: | |
| = | (tag_ParamPol(P,type_P):tP,tag_ParamPol(Q,type_Q):tQ) = bool: | |
| + | (tag_ParamPol(P,type_P):tP,tag_ParamPol(Q,type_Q):tQ) = tag_ParamPol: | |
| + | (tag_Param(p,type_p),tag_Param(q,type_q)) = tag_ParamPol: | |
| + | (tag_ParamPol(P,type_P),tag_Param(q,typeq)) = tag_ParamPol: | |
| - | (tag_ParamPol(P,type)) = tag_ParamPol: (minus_1*P,type) | |
| - | (tag_Param(p,type))= tag_ParamPol: (minus_1*p,type) | |
| - | (tag_ParamPol(P,type_P),tag_ParamPol(Q,type_Q)) = tag_ParamPol: | |
| - | = tag_ParamPol: | |
| - | (tag_Param(p,typep),tag_Param(q,typeq))=tag_ParamPol: | |
| * | (Split w,tag_ParamPol(P,type)) = tag_ParamPol: (w*P,type) | |
| * | (Split w,tag_Param(p,type)) = tag_ParamPol: (w*p,type) | |
| = | (tag_ParamPol(P,type_P),tag_Param(q,typeq)) = bool: | |
| infinitesimal_character | (tag_Param(p,)) = ratvec: | |
| has_infinitesimal_character | (ParamPol P) = bool: | |
| infinitesimal_character | (tag_ParamPol (P,)) = ratvec: | |
| tau | (tag_Param (p,)) = [int]: tau(p) | |
| in_tau | (int s,tag_Param(p,)) = bool: let (,b)= tau_bitset(p) in b(s) | |
| in_tau_complement | pair) = bool: not(in_tau(pair)) | |
| tau_complement | (tag_Param(p,)) = [int]: tau_complement(p) | |
| status | (int s,tag_Param (p,)) = int: status(s,p) | |
| branch | (tag_Param(p,type), int bound) = KTypePol: |