Category Archives: Groups & Representations

Dimensions of su(n) irreps from Young Tableaux

Posted on November 3, 2010 by Raghu Mahajan

See this and this for some background. While considering a Young diagram of an irrep of , put an in the top left box. Starting from here, fill out all the boxes with numbers adding one each time you go … Continue reading →

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Labelling the Irreducible Representations of su(n)

Posted on November 3, 2010 by Raghu Mahajan

In this post, I specify all the irreducible representations (irreps) of and over a complex carrier space. For , the answer is that the irreps are labelled by a single whole number , with the dimension of the representation labelled … Continue reading →

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Irreducible Representations of the Symmetric Group

Posted on November 3, 2010 by Raghu Mahajan

There is cute way to find the dimensions of all the irreducible representations (irreps) of the symmetric group , the group of permutations of symbols. Every permutation can be written as a product of cycles, and two permutations with identical … Continue reading →

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Finite Subgroups of SO(3)

Posted on May 24, 2010 by Raghu Mahajan

The only finite subgroups of are the following: Cyclic group of any finite order Dihedral group of any order (note that reflection about an axis in 2-dimensions can be obtained by a proper rotation in the embedding 3-space) The group … Continue reading →

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Associative Algebras and Group Algebras

Posted on May 24, 2010 by Raghu Mahajan

We always work over the field of complex numbers . All vector spaces in this post are assumed to be finite-dimensional. An associative algebra is a vector space together with an associative product operation . We always assume that this … Continue reading →

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Free Abelian Groups and Free Groups

Posted on May 23, 2010 by Raghu Mahajan

Given a set , finite or infinite, the free abelian group with basis is defined to be the set of all finite integer-linear combinations of the elements of . That is, every element of the group looks like for some … Continue reading →

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