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This is a Sage worksheet for finding RoCK blocks of Ariki-Koike algebras and related algebras. This is the best starting place if you want to test a few examples.

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License: GPL3
ubuntu2004
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load("RoCK-test.sage") #You need to load this to make things work.
#If you have a specific block to test, you enter it below
#This sets up the example from page 11 of https://arxiv.org/pdf/2206.14720.pdf
e=4 #quantum characteristic
multicharge=(2,0,1) #multicharge: the program expects these to be in 0,...,e-1
al={ 0: 25, 1: 32, 2: 34, 3: 32} #this specifies the number of boxes with each residue in your block
dom=find_dom_w_chamber(al,e,multicharge)[1] #This finds the dominant weight in the orbit of al
dom
{0: 13, 1: 13, 2: 13, 3: 12} 
test_RoCK_verbose(al,e,multicharge)
The pair [1, 2] is OK since 9/2 is not between 2 and -2 . The pair [1, 3] is OK since -9/4 is not between 3 and -2 . The pair [2, 3] is OK since -27/4 is not between 3 and -2 . There's a problem with [1, 4] since 3 > 9/4 > -2 . The pair [2, 4] is OK since -9/4 is not between 3 and -2 . The pair [3, 4] is OK since 9/2 is not between 2 and -2 . False 
RoCKs=all_RoCKs(al,e,multicharge) #This will find minimal RoCK blocks in the orbit of al for every Weyl chamber.
RoCKs
{(3/4, 1/2, 1/4, 0): {0: 37, 1: 34, 2: 27, 3: 34}, (3/4, 1/2, 0, 1/4): {0: 37, 1: 34, 2: 27, 3: 34}, (3/4, 1/4, 1/2, 0): {0: 34, 1: 42, 2: 45, 3: 42}, (3/4, 1/4, 0, 1/2): {0: 34, 1: 42, 2: 45, 3: 42}, (3/4, 0, 1/2, 1/4): {0: 37, 1: 29, 2: 37, 3: 39}, (3/4, 0, 1/4, 1/2): {0: 37, 1: 29, 2: 37, 3: 39}, (1/2, 3/4, 1/4, 0): {0: 37, 1: 34, 2: 27, 3: 34}, (1/2, 3/4, 0, 1/4): {0: 37, 1: 34, 2: 27, 3: 34}, (1/2, 1/4, 3/4, 0): {0: 37, 1: 39, 2: 37, 3: 29}, (1/2, 1/4, 0, 3/4): {0: 37, 1: 39, 2: 37, 3: 29}, (1/2, 0, 3/4, 1/4): {0: 45, 1: 42, 2: 34, 3: 42}, (1/2, 0, 1/4, 3/4): {0: 45, 1: 42, 2: 34, 3: 42}, (1/4, 3/4, 1/2, 0): {0: 34, 1: 42, 2: 45, 3: 42}, (1/4, 3/4, 0, 1/2): {0: 34, 1: 42, 2: 45, 3: 42}, (1/4, 1/2, 3/4, 0): {0: 37, 1: 39, 2: 37, 3: 29}, (1/4, 1/2, 0, 3/4): {0: 37, 1: 39, 2: 37, 3: 29}, (1/4, 0, 3/4, 1/2): {0: 27, 1: 34, 2: 37, 3: 34}, (1/4, 0, 1/2, 3/4): {0: 27, 1: 34, 2: 37, 3: 34}, (0, 3/4, 1/2, 1/4): {0: 37, 1: 29, 2: 37, 3: 39}, (0, 3/4, 1/4, 1/2): {0: 37, 1: 29, 2: 37, 3: 39}, (0, 1/2, 3/4, 1/4): {0: 45, 1: 42, 2: 34, 3: 42}, (0, 1/2, 1/4, 3/4): {0: 45, 1: 42, 2: 34, 3: 42}, (0, 1/4, 3/4, 1/2): {0: 27, 1: 34, 2: 37, 3: 34}, (0, 1/4, 1/2, 3/4): {0: 27, 1: 34, 2: 37, 3: 34}} 
RoCKs.values() #this collects just the blocks, forgetting the associated Weyl chamber.
dict_values([{0: 37, 1: 34, 2: 27, 3: 34}, {0: 37, 1: 34, 2: 27, 3: 34}, {0: 34, 1: 42, 2: 45, 3: 42}, {0: 34, 1: 42, 2: 45, 3: 42}, {0: 37, 1: 29, 2: 37, 3: 39}, {0: 37, 1: 29, 2: 37, 3: 39}, {0: 37, 1: 34, 2: 27, 3: 34}, {0: 37, 1: 34, 2: 27, 3: 34}, {0: 37, 1: 39, 2: 37, 3: 29}, {0: 37, 1: 39, 2: 37, 3: 29}, {0: 45, 1: 42, 2: 34, 3: 42}, {0: 45, 1: 42, 2: 34, 3: 42}, {0: 34, 1: 42, 2: 45, 3: 42}, {0: 34, 1: 42, 2: 45, 3: 42}, {0: 37, 1: 39, 2: 37, 3: 29}, {0: 37, 1: 39, 2: 37, 3: 29}, {0: 27, 1: 34, 2: 37, 3: 34}, {0: 27, 1: 34, 2: 37, 3: 34}, {0: 37, 1: 29, 2: 37, 3: 39}, {0: 37, 1: 29, 2: 37, 3: 39}, {0: 45, 1: 42, 2: 34, 3: 42}, {0: 45, 1: 42, 2: 34, 3: 42}, {0: 27, 1: 34, 2: 37, 3: 34}, {0: 27, 1: 34, 2: 37, 3: 34}]) 
e=3 #quantum characteristic
multicharge=(0,0,1,2) #multicharge: the program expects these to be in 0,...,e-1
al={ 0: 3,1:2,2:2}
all_RoCKs(al,e,multicharge)
{(2/3, 1/3, 0): {0: 11, 1: 18, 2: 18}, (2/3, 0, 1/3): {0: 23, 1: 22, 2: 14}, (1/3, 2/3, 0): {0: 23, 1: 14, 2: 22}, (1/3, 0, 2/3): {0: 23, 1: 22, 2: 14}, (0, 2/3, 1/3): {0: 23, 1: 14, 2: 22}, (0, 1/3, 2/3): {0: 11, 1: 18, 2: 18}} 
weight_from_block({0: 3, 1: 2, 2: 2},e,multicharge,9)
weight_from_block({0: 11, 1: 18, 2: 18},e,multicharge,9)
weight_from_block({0: 23, 1: 22, 2: 14},e,multicharge,9)
weight_from_block({0: 23, 1: 14, 2: 22},e,multicharge,9)
[[12, 10, 8], [11, 10, 9]] [[4, 10, 16], [11, 10, 9]] [[12, 18, 0], [11, 10, 9]] [[20, 2, 8], [11, 10, 9]]