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Re: Deformed Matrix Product

• To: mathgroup at smc.vnet.net
• Subject: [mg72226] Re: Deformed Matrix Product
• From: "Ray Koopman" <koopman at sfu.ca>
• Date: Fri, 15 Dec 2006 07:06:06 -0500 (EST)
• References: <eloom4$mu6$1@smc.vnet.net>

simoseve at gmail.com wrote:
> Dear All,
>
> I would like to implement a form of matrix product called deformed
> matrix product.
>
> The definition can be found at page 2 of
>
> http://ipnweb.in2p3.fr/lptms/membres/pzinn/semi/ium.pdf
>
> P. Zinn-Justin, Combinatorics of the Brauer Loop scheme.
>
> Is there any good samaritan out there that knows how to do it?
>
> Thanks a lot for your time and kind consideration.
>
> Simone Severini

First define a cyclic range function:

cyc[i_,k_,n_] := If[i <= k, Range[i,k], Join[Range[i,n],Range[k]] ]

Then the deformed product is given by:

defprod[P_,Q_] := With[{n = Length@P},
Table[ P[[i,cyc[i,k,n]]].Q[[cyc[i,k,n],k]], {i,n},{k,n}]]