Script Reference
stable.at
Stable virtual characters and stable distributions for real reductive groups.
Mathematical background
A virtual character is stable if it is invariant under all inner twists. Stable characters arise in the theory of endoscopy and the stable trace formula.
Definitions
| Name | Signature | Description |
|---|---|---|
| evaluate_at_1 | ([i_poly] v)= vec: for w in v do evaluate_at_1(w) od | |
| evaluate_at_1 | (i_poly_mat M) = mat: | |
| left_kernel | = cokernel@mat { defined as |cokernel| in basic.at } | defined as |cokernel| in basic.at |
| column | (i_poly_mat M,int j) = [i_poly]: for row in M do row[j] od | |
| null_poly_mat | (int r,int c) = i_poly_mat: | |
| mat_as_poly_mat | (mat A) = i_poly_mat: | |
| * | (mat A,i_poly_mat B) = i_poly_mat: mat_as_poly_mat(A)*B | |
| has_infinitesimal_character | ([Param] params) = bool: | |
| make_regular | (Param p) = Param: | |
| make_param_pol | (RealForm G,[int] coefficients,[Param] params) = ParamPol: | |
| permutation_matrix_sort | S) = mat: | |
| in_tau | (int s,Param p) = bool: { whether s is in tau(p) } | whether s is in tau(p) |
| in_tau | ([int] S,Param p) = bool: { whether $S\subset\tau(p)$ } | whether $S\subset\tau(p)$ |
| in_tau | S,Param p) = bool: true { whether $\emptyset\subset\tau(p)$ } | whether $\emptyset\subset\tau(p)$ |
| in_tau_complement | (int s,Param p) = bool: { whether s not in tau(p) } | whether s not in tau(p) |
| in_tau_complement | ([int] S,Param p) = bool: { whether $S\cap\tau(p)$ empty } | whether $S\cap\tau(p)$ empty |
| Psi_irr | ([Param] params,[int] S) = [Param]: | |
| parameters_tau_containing | ([int] S,[Param] params) = [int]: | |
| parameters_tau_contained_in_complement | ([int] S,[Param] params) = [int]: | |
| duality_permutation | ([Param] B) = [int]: let (,perm)=dual_block(B) in perm | |
| dual_parameters | ([int] S,[Param] B) = [int]: | |
| parameters | ([int] S,[Param] B) = [int]: | |
| parameters_singular | ([int] S,[Param] B) = [Param]: | |
| lengths_signs | ([Param] params) = [int]: | |
| lengths_signs_matrix | ([Param] params) = mat: | |
| lengths_signs | ([int] S,[Param] B) = [int]: | |
| lengths_signs_matrix | ([int] S,[Param] B) = mat: | |
| dual_parameters_matrix | ([int] S,[Param] B) = mat: | |
| dual_parameters_matrix | ([Param] B) = mat: dual_parameters_matrix([int]:[],B) | |
| dual_parameters_matrix | ([Param] B, [int] T) = mat: | |
| dual_parameters_standard_basis_poly_mat | ([Param] B) = i_poly_mat: | |
| dual_parameters_standard_basis | ([Param] B) = mat: | |
| dual_parameters_standard_basis | ([int] S,[Param] B) = mat: | |
| indices | ([Param] B,[Param] subset) = [int]: for p in subset do find(B,p) od | |
| subspace_injection_matrix | ([Param] B,[Param] subset) = mat: | |
| get_y | ([Param] B) = [int]: | |
| stable_at_regular | ([Param] B) = mat: | |
| vanishing | ([int] S,[Param] B) = mat: | |
| kernel_vanishing | ([int] S,[Param] B) = mat: kernel(^vanishing(S,B)) | |
| stable_at_singular_unsorted | ([int] S,[Param] B) = (mat,[Param]): | |
| stable_at_singular | ([int] S,[Param] B) = (mat,[Param]): | |
| stable_at_singular | ([int] S,[Param] B,[Param] subset_in) = (mat,[Param]): | |
| stable_sums | singular_parameters)=[(mat,[Param])]: | |
| stable_sums_partial | singular_parameters)= | |
| print_stable_at_singular_unsorted | ([int] S,[Param] B) = void: | |
| print_stable_at_singular | ([int] S,[Param] B) = void: | |
| stable_at_singular | ([int] S,[Param] B,[Param] subset_in) = (mat,[Param]): | |
| print_stable_at_singular | ([int] S,[Param] B,[Param] subset) = void: | |
| stable | ([Param] params) = (mat,[Param]): | |
| print_stable | params) = void: | |
| stable_test_Aq_packet | (RealForm G,ComplexParabolic P) = void: | |
| stable_test_Aq_packet | (RealForm G,[int] complex_parabolic) = void: | |
| * | v,[Param] params)= | |
| * | M,[Param] params)=for v in M do v*params od | |
| printParamPol | P)=void: | |
| print_sums | ([(mat,[Param])] list)=void: | |
| print_stable_sums | list)=void: | |
| print_stable_sums | lists)=void: |