The Standard Form of a Representation Finite Algebra NUMDAM Archive Numdam

Instructions and help about The Standard Form Of A Representation finite Algebra NUMDAM Archive Numdam

here we're going to begin looking at representations of groups and to be more specific we're going to look at complex finite dimensional representations of groups so let's look at a definition so a representation of a group G is a homomorphism fee from G to GL v where v is a finite dimensional vector space over C and let's just recall that GL V is the group of all invertible linear transformations from V to V in other words the general linear group of V and then also we'll say that the degree of the representation is just the dimension of the underlying vector space next the kind of standard way to think about n dimensional vectors are column vectors in other words see n and so if V is C n in that case we have GL v is GL n C in other words it's the group of invertible n by n complex matrices so if we have a degree in representation of a group we really have a way of assigning every element from that group to an N by n matrix okay and then here's a little bit more notation before we loo