Special routines for wreath products |

INT init_kranz(a) OP a;initializes a KRANZ object

`a`

.
Given a PERMUTATION of *n* elements and a VECTOR of length *n* you can
compute the corresponding KRANZ object with

INT m_perm_vector_kranz(p,v,a) OP p,v,a;

`p`

stands for the PERMUTATION, `v`

for the VECTOR
and `a`

for the KRANZ object.
INT scan_kranz(a) OP a;can be used to scan the KRANZ object

`a`

.
INT mult_kranz_kranz(a,b,c) OP a,b,c;you can multiply two KRANZ objects

`a`

and `b`

according to the definition given above
to get `c`

.
There are various routines for selecting the different parts of a KRANZ object.

OP s_kr_g(a) OP a; OP s_kr_v(a) OP a; OP s_kr_i(a,i) OP a; INT i; INT s_kr_gli(a) OP a; OP s_kr_gl(a) OP a; OP s_kr_gi(a,i) OP a; INT i; S_KR_GI(a,i) OP a; INT i; INT s_kr_gii(a,i) OP a; INT i; S_KR_GII(a,i) OP a; INT i; OP s_kr_ij(a,i,j) OP a; INT i,j; S_KR_IJ(a,i,j) OP a; INT i,j; INT s_kr_iji(a,i,j) OP a; INT i,j; S_KR_IJI(a,i,j) OP a; INT i,j;In all these cases

`a`

is a KRANZ object.
`s_kr_g`

stands for `select_kranz_grobpermutation`

, which
selects the first part (the PERMUTATION part) of `a`

.
`s_kr_v`

selects the VECTOR part (the second part) of `a`

.
`s_kr_i`

selects the `i`

-th entry of the VECTOR part of
`a`

. `s_kr_gli`

returns the integervalue of the length
of the PERMUTATION part of `a`

.
`s_kr_gl`

is the length (as an INTEGER object) of the
PERMUTATION part of `a`

.
`s_kr_gi`

selects the `i`

-th entry of the PERMUTATION
part of `a`

.
`s_kr_gii`

returns the integervalue of the
`i`

-th entry of the PERMUTATION part of `a`

.
In order to use the next two routines you must take care
that the entries of the VECTOR part of `a`

are also
PERMUTATION objects.
`s_kr_ij`

selects the `j`

-th entry of the
`i`

-th entry of the VECTOR part of `a`

.
`s_kr_iji`

returns the integervalue of the
`j`

-th entry of the
`i`

-th entry of the VECTOR part of `a`

.
Given two permutation groups *G* and *H* by their
sets of generators, we can compute the generators
of *H wr G* with the following routine:

INT gen_full_mon_group(a,b,c) OP a,b,c;

`a`

and `b`

are the VECTORs of generators
of `c`

is a VECTOR object, where
each entry is a KRANZ object. These entries are the
generators of The generators of the plethysm
*H pleth G* can be computed
with

INT gen_plethysm(a,b,c) OP a,b,c;where

`a`

and `b`

are the VECTORS of
generators of `c`

is a VECTOR of
generators of The permutation representation of a KRANZ object where the entries of the VECTOR part are PERMUTATIONs is computed by

INT t_kranz_plethysm(a,b) OP a,b;

`a`

is a KRANZ object where all the entries of
the VECTOR part are PERMUTATIONs of the same degree.
`b`

is a PERMUTATION object, the induced
permutation in form of the plethysm.
harald.fripertinger@kfunigraz.ac.at,

last changed: November 19, 2001

Special routines for wreath products |