Atlas of Lie Groups and Representations

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atlas Library · Script File

tensor_product.at

Source
atlas-scripts/tensor_product.at (160 lines)
Definitions
28
Loads
Loaded by
hodge_K_type_formula.at hodge_tensor.at GK_dimension.at

Definitions in source order

N

L7N = 100
cutoff for branching

also defined in structure_constants.at

K_type_formula

L9K_type_formula (KType t) = KTypePol
without height bound

also defined in basic.at

given a set of rational vectors all of the same length
for each of the 2^n subsets return the sum
application: given a subalgebra u this computes all the weights of wedge(u)
L12

dimension

L18dimension (KTypePol P) = int
add up the dimensions of terms in a KTypePol

also defined in basic.at, finite_dimensional.at, K_highest_weights.at, nilpotent_orbits.at, character_tables.at, W_reps_type_BC.at, exceptional.at

dimension_u_cap_s

L21dimension_u_cap_s(Parabolic P) = int

dimension_wedge_u_cap_s

L22dimension_wedge_u_cap_s(Parabolic P) = int

add_weight

L25add_weight (Param p,ratvec H) = KTypePol
simply add H to p.lambda and standardize the result

also in this file at line 32, line 37, line 40, line 50, line 66

add_weights

L28add_weights (Param p,(KGBElt->[ratvec]) weights) = KTypePol

also in this file at line 44, line 55, line 61, line 70

add_weight 3 overloads

L32add_weight (ParamPol P,ratvec H) = KTypePol
simply add H to each term of P, standardize the results
L37add_weight (ParamPol P,(KGBElt->ratvec) f) = KTypePol
given a function f: KGBElt -> ratvec, replace each p=(x,lambda,nu) with
standard(parameter(x,lambda+f(x),nu))
L40add_weight (ParamPol P,(KGBElt->ratvec) f) = KTypePol

also in this file at line 25, line 50, line 66

add_weights

L44add_weights (ParamPol P,(KGBElt ->[ratvec]) weights) = KTypePol
same as previous, applied to a ParamPol

also in this file at line 28, line 55, line 61, line 70

add_weight

L50add_weight (KTypePol P,(KGBElt->vec) f) = KTypePol
this is what probably should be preferred to the above functions

also in this file at line 25, line 32, line 37, line 40, line 66

add_weights 2 overloads

L55add_weights (KTypePol P,(KGBElt ->[vec]) weights) = KTypePol
same as previous, applied to a ParamPol
L61add_weights (ParamPol P,(KGBElt ->[ratvec]) f) = KTypePol

also in this file at line 28, line 44, line 70

add_weight

L66add_weight (KType t,(KGBElt->vec) f) = KTypePol
add weight (given by function f) to K_type_formula(mu)

also in this file at line 25, line 32, line 37, line 40, line 50

add_weights

L70add_weights (KType t,(KGBElt->[vec]) f) = KTypePol
add weights (given by function f) to K_type_formula(mu)

also in this file at line 28, line 44, line 55, line 61

tensor_product 2 overloads

L79tensor_product(KType t,(KGBElt -> [vec]) weights,int bound) = KTypePol
given a K_type mu and a function f:KGB->[vec],
 compute mu\otimes (K-type given by the weights)
 the bound here shouldn't be necessary: add_weights(mu,weights) is a finite sum
 of K-types, the bound just needs to be big enough to get them all
see the next command
L83tensor_product(KType t,(KGBElt -> [vec]) weights) = KTypePol
choose the bound appropriately: not at all sure this is right

also defined in finite_dimensional.at, character_tables.at

tensor_product_u_cap_s

L92tensor_product_u_cap_s (KType mu_L,Parabolic P,int bound) = KTypePol
The Main Function
L=Levi(P), P=theta-stable parabolic in G
mu_L=L\cap K-type
compute mu_L\otimes wedge(u\cap s)
this is simply branch_std(add_weights(mu_L,weights),bound)

tensor_product_wedge_k_u_cap_s 2 overloads

L95tensor_product_wedge_k_u_cap_s (KType mu_L,Parabolic P,int bound,int k) = KTypePol
L101tensor_product_wedge_k_u_cap_s (KType mu_L,Parabolic P,int k) = KTypePol

test 3 overloads

L105test (KType mu_L,Parabolic P, int bound) = bool
a few dimension tests
L109test ([KType] lktypes,Parabolic P, int bound) = bool
L115test(int bound,Parabolic P) = bool

also defined in test_unitarity.at, all_finite_order.at, nilpotent_centralizer.at, sommers.at, nilpotent_posets.at

test_long

L118test_long([KType] lktypes,Parabolic P,int bound) = void

wt_mult

L136wt_mult (RealForm G, vec FD, vec wt) = int
Multiplicity of the weight wt in the finite dimensional algebraic rep'n with
highest weight FD

add_wt_to_param

L144add_wt_to_param (Param p, vec H) = ParamPol
Parameter obtained from adding the weight H to both lambda and nu, which may
be non-dominant; and finalize

tensor_with_fd

L150tensor_with_fd (Param p, vec FD) = ParamPol
Compute the tensor product of an irreducible representation with a finite
dimensional algebraic representation of highest wwight FD

Generated from atlas-scripts at commit 648506c (2026-10-13).