My OperaStatus 28 nov 2005
Sunday, November 27, 2005 11:41:04 PM
From Lecture 1.2 (Schur's Lemma) p8
"Our first goal, in analyzing the representations of any group, will therefore be:
(i) Describe all the irreducible representations of G.
Once we have done this, there remains the problem of carrying out in practice the description of a given representation in these terms. Thus, our second goal will be:
(ii) Find techniques for giving the direct sum decomposition, and in particular determining the multiplicities a(i) of an arbitrary representation V. ..."
Mapping (i) and (ii) to my situation: (i) is ok, (ii) could be problematic. Lectures 1 and 2 of the book are about (irreducible) representations, characters and the most important theorems about these topics. My understanding of the subject is much than one week ago. I still need more practice. Will do so.
"Our first goal, in analyzing the representations of any group, will therefore be:
(i) Describe all the irreducible representations of G.
Once we have done this, there remains the problem of carrying out in practice the description of a given representation in these terms. Thus, our second goal will be:
(ii) Find techniques for giving the direct sum decomposition, and in particular determining the multiplicities a(i) of an arbitrary representation V. ..."
Mapping (i) and (ii) to my situation: (i) is ok, (ii) could be problematic. Lectures 1 and 2 of the book are about (irreducible) representations, characters and the most important theorems about these topics. My understanding of the subject is much than one week ago. I still need more practice. Will do so.
