[GAP Forum] Casimir Invariants of Lie Algebras

Dear gap-forum, Is it possible to calculate Casimir invariants of Lie algebras? Alternatively can you calculate the center of the the Universal Enveloping Algebra? Here's an attempt that didn't work : gap L:= SimpleLieAlgebra( B, 2, Rationals );; gap UL:= UniversalEnvelopingAlgebra(

[GAP Forum] tensor product of lie algebra representations

Dear gap-forum, I have question regarding tensor products of representations of semisimple lie algebra. It's easier to setup the question with an example : # first define the Lie algebra A2 L := SimpleLieAlgebra(A,2,Rationals); # define V1 as module with highest weight

Re: [GAP Forum] algebra mapping problem

Dear Willem and gap-forum, That's too bad. A simple substitution rule or evaluation map for algebras would be a useful feature to have in GAP. BTW, this problem occurs outside the WeylAlg package. Here's another simple example with lie algebras:

[GAP Forum] subalgebras of simple lie algebras

Dear gap-forum, Is there a way to look for subalgebras of certain type in a simple lie algebra. Interestingly enough the example in the documentation is very close to what I'm looking for : gap L:= SimpleLieAlgebra( E, 8, Rationals );; gap b:= BasisVectors( Basis( L ) );; gap K:=

[GAP Forum] unsupported functions in new release (4.4.10)

Dear gap forum,   I just installed the latest version of gap4 (4.4.10) and tried it with some old code (which worked with previous versions). It looks like the following two functions are no longer supported :    FromTheLeftCollector  PcpGroupByCollector   I get this error :   Syntax error:

[GAP Forum] semisimple type and chevalley basis

Dear gap-forum, I define a lie algebra which I know to be equivalent to type A1. I was hoping to have gap calculate a chavalley basis for this, but this doesn't seem to be possible; even though gap recognizes the algebra as A1 (using SemiSimpleType). Is there a way around this? Thanks, R.N.

[GAP Forum] polynomial invariants of weyl groups

Dear gap-forum, I'm trying to calculate the polynomial invariants of weyl groups (associated with simple lie algebras over the complex field, in the rep corresponding to the rank of the algebra...). Does anyone know of any existing packages that can help? (CHEVIE has some partial results, but it

[GAP Forum] next gap release

Dear gap-forum,   I read from another thread that there will be a new release of gap. I'd like to request a small feature that can hopefully be included : when assigning names to the generators of an algebra  instead of :   AlgebraByStructureConstants( R, sctable, name1, name2, ... )   this would

[GAP Forum] naming convention for basis of highest weight modules

Dear gap-forum, Is the naming convention for the basis of highest weight modules described anywhere? For example : gapL:=SimpleLieAlgebra(A,2,Rationals);; gapM1:=HighestWeightModule(L,[1,0]);; gapB1:=Basis(M1);; gapM2:=TensorProductOfAlgebraModules(M1,M1);; gapB2:=Basis(M2);; gap

Re: [GAP Forum] Algebras

Dear Max and forum, I have used GBNP successfully in the past with e.g. BMW algebras. But of course anything dealing with Gröbner bases in free associative algebras is bound to hit some snags at some point... But in the examples you list below, GBNP should easily work... If you tell us

Re: [GAP Forum] Algebras

Dear Mohamed and forum, the Weyl algebra and the exterior algebra (including GB computations) are supported through the homalg project’s interface to Singular/Plural/SCA. The clifford algebra can also be supported easily: gap LoadPackage( RingsForHomalg ); true This seems to load ok but when

[GAP Forum] ELIAS package for Lie algebra reps

Dear forum, I ran across this page which references a GAP4 package used to construct finite dimensional representations of Lie algebras (ELIAS). ftp://ftp.gap-system.org/pub/gap/NEU/Info/oldevents.html I didn't find ELIAS in the list of packages. Does anyone know if this is still available.

[GAP Forum] semsimple algebras and subalgebras

Dear forum, I am using the sla package to do calcualtions with semisimple lie algebras and their subalgebras. The calculations involve decomposing an irrep of the main algebra into irreps of one of its subalgebras. The Branching functions works great at providing this data. I'd like to extract

Re: [GAP Forum] semsimple algebras and subalgebras

. On Monday, February 17, 2014 12:39 AM, Willem de Graaf degr...@science.unitn.it wrote: Dear R.N. Tsai, You asked: I'd like to identify the subalgebra irreps with concrete subspaces of the main algebra. Is there a (hopefully simple) way to extract this information? Not directly, however

[GAP Forum] value of casimir elements

Dear forum, For a simple lie algebra (of rank n) and a highest weight representation (w1,...wn); is it possible to calculate the values of the n casimir invariants (as functions of w1,...,wn) within GAP or any of its packages? Thanks, R.N.   ___ Forum

[GAP Forum] superlie algebras

Dear GAP forum, Is there anything in gap or its packages that deals with superlie algebras?I'm interested mainly in the orthosymplectic algebras; if I can get a way todefine their structure (either as a multiplication table of generators or as a quotient of a free algebra)I think I can build on

Re: [GAP Forum] saving variables to a file

Thanks for the response Max,The matrices are over GF(2), so hopefully they can be managed more efficiently than generic matrices.R.N From: Max Horn <m...@quendi.de> To: R.N. Tsai <r_n_t...@yahoo.com> Cc: GAP Forum <fo...@gap-system.org> Sent: Tuesday, June 14, 2016 2:

Re: [GAP Forum] saving variables to a file

.uk> To: R.N. Tsai <r_n_t...@yahoo.com> Cc: GAP Forum <fo...@gap-system.org> Sent: Tuesday, June 14, 2016 4:19 AM Subject: Re: [GAP Forum] saving variables to a file Dear all, On Tue, Jun 14, 2016 at 11:01:55AM +0200, Max Horn wrote: > > On 14 Jun 2016, at 05:52, R.N. Tsai &l

Re: [GAP Forum] saving variables to a file

.bmp file in matlab so this could be one way to passthe matrices between the two.Thanks for your help.R.N. From: Stefan Kohl <ste...@mcs.st-and.ac.uk> To: R.N. Tsai <r_n_t...@yahoo.com> Cc: Max Horn <m...@quendi.de>; GAP Forum <fo...@gap-system.org> Sent: Wednesday,

[GAP Forum] running with grape package under windows 64

Dear GAP forum,I'm doing some calculations with gap+grape package under windows. Things work fine with the gap32 version, but grape doesn't seem to workwith gap64. The graphs I'm working with are very large and I would liketo run gap64 with 16GBytes memory. Is there a 64 bit version of

Re: [GAP Forum] running with grape package under windows 64

an example :    gap>Process(H1); #finishes ok; no variables saved...   gap>Process(H2); #comes back with memory problem   if I exit gap and start again   gap>Process(H2); #now this works without memory problem. Thanks for your help. R.N. From: Alexander Konovalov <alexander.konova...

Re: [GAP Forum] running with grape package under windows 64

d to look at larger matrices soon so any othersuggestions for efficiency are appreciated. Regards,R.N. From: "Bailey, Robert F." <rbai...@grenfell.mun.ca> To: R.N. Tsai <r_n_t...@yahoo.com> Cc: GAP Forum <fo...@gap-system.org> Sent: Thursday, July 7, 2016 1:54

Re: [GAP Forum] formatted "Print"

matted "Print" Dear GAP Forum, concerning the question by R.N. Tsai > Is there a way to do a formatted print in GAP? > Something equivalent to this for example :  %6d or %-6d  to print an > alignedfixed width 6 bit integer(these are c examples but are used in > other lang

Re: [GAP Forum] Building Variables

Dear GAP Forum and Sara, I use this sometimes : A:=List([1..71],k->Concatenation("a",String(k))); then A[1]...A[71] are the variables... R.N. From: Sara Dikson To: fo...@gap-system.org Sent: Saturday, September 3, 2016 8:04 AM Subject: [GAP Forum] Building

[GAP Forum] formatted "Print"

Dear GAP forum, Is there a way to do a formatted print in GAP? Something equivalent to this for example :  %6d or %-6d  to print an alignedfixed width 6 bit integer(these are c examples but are used in other languages too). Thanks,R.N. ___ Forum

[GAP Forum] extending database in SLA package

Dear GAP forum, I'm using Willem de Graaf's SLA package to study lie algebras and their sublagebras.I know that  the package includes a precomputed database listed here : gap> SSSTypes();[ "A1", "A2", "B2", "G2", "A3", "B3", "C3", "A4", "B4", "C4", "D4", "F4", "A5", "B5", "C5", "D5", "A6",

Re: [GAP Forum] creating directories

"CreateDir()" is the simplest way and it did work on Windows; I'm trying to make my code OS independent so it would be nice if  it is made more official in a future release.Thanks,R.N. From: Max Horn <m...@quendi.de> To: R.N. Tsai <r_n_t...@yahoo.com> Cc: GAP Forum