1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
|
COMMENT:
GROUP ALGEBRA
-------------
This is a variant of the POLYNOM type, the name of this class
of objects is GRAL (for group algebra). The type of the self part
is a permutation instead of a vector as in the case of POLYNOM.
So a general object of type GRAL is a list of permutations with
arbitrary coefficents.
For the selection of parts you have to use the macros for polynom
objects (up to now)
There are two routines for the construction
NAME:
m_skn_gral
SYNOPSIS:
INT m_skn_gral(OP self, OP koeff, OP next, OP res)
DESCRIPTION:
same as m_skn_po in the file poly.doc
NAME:
b_skn_gral
SYNOPSIS:
INT b_skn_gral(OP self, OP koeff, OP next, OP res)
DESCRIPTION:
same as b_skn_po in the file poly.doc
NAME:
hplus_hecke
SYNOPSIS:
INT hplus_hecke(OP a,b)
NAME:
hplus
SYNOPSIS:
INT hplus(OP a,b)
DESCRIPTION:
computes the sum over all horizonatl permutation of a
TABLEAUX object a. cf. Mueller: Darstellungstheorie
The result is a GRAL object.
BUG:
only for TABLEAUX of PARTITION shape
NAME:
vminus_hecke
SYNOPSIS:
INT vminus_hecke(OP a,b)
NAME:
vminus_tabloid
SYNOPSIS:
INT vminus_tabloid(OP a,b)
NAME:
vminus
SYNOPSIS:
INT vminus(OP a,b)
DESCRIPTION:
computes the signed sum over all vertical permutations of a
TABLEAUX object a. cf. Mueller: Darstellungstheorie
The result is a GRAL object.
BUG:
only for TABLEAUX of PARTITION shape
NAME:
random_gral
SYNOPSIS:
INT random_gral(OP a,b)
DESCRIPTION:
computes a random element of the group algebra. The degree
of the involved permutations is given by the INTEGER object a. The
coefficents are INTEGER object given by random_integer, so they lay
between -10 and 10. There are maximal ten terms.
NAME:
operate_gral_polynom
SYNOPSIS:
INT operate_gral_polynom(OP a,b,c)
DESCRIPTION:
applies the element of the group algebra a to a
POLYNOM b, and the result is a new POLYNOM c
NAME:
vertikal_sum
SYNOPSIS:
INT vertikal_sum(OP a,b)
DESCRIPTION:
computes the sum over all permutations of degree a,
the result is the object b, a element of type GROUPALGEBRA
NAME:
garnir
SYNOPSIS:
INT garnir(OP tab,v,x,res)
DESCRIPTION:
cf. James/Kerber p.301, tab is a TABLEAUX object
v and x a VECTOR objects of INTEGERS containing entries of
different coulmns, the result is a GROUPALGEBRA object.
COMMENT:
GENERAL ROUTINES
----------------
add
add_apply
addinvers
comp
copy
fprint
fprintln
freeall
freeself
mult
objectread
objectwrite
print
println
scan
tex
|
