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Sep
24 |
awarded | Autobiographer |
Jun
11 |
revised |
Previous derivation of a combinatorial formula for the fundamental representations of $A_{n-1}$
deleted 7 characters in body |
Jun
11 |
asked | Previous derivation of a combinatorial formula for the fundamental representations of $A_{n-1}$ |
Jun
7 |
comment |
Symmetric powers of Schur polynomials
Many thanks Steven. I will look into this interface |
Jun
7 |
accepted | Symmetric powers of Schur polynomials |
May
31 |
comment |
Symmetric powers of Schur polynomials
Per Alexandersson: I do not believe that there is such a rule for composition of Schur functions. There exists the Littlewood-Richardson rule for multiplication of Schur functions that can be phrased as you say, but this is surely known to you. |
May
29 |
comment |
Symmetric powers of Schur polynomials
Let's consider the representation of $A_2$ i.e., $\mathfrak{sl}_3$ given by $\lambda = (3,2)$ so this has highest weight $\omega_1 + 2\omega_2$ where $\omega_i$ is the $i$th fundamental weight of $A_2$, and I write an arbitrary irreducible representation of $A_2$ as $\Gamma_{a,b}$ where $\lambda = a\omega_1 + b\omega_2$ is the highest weight. Then $Sym^2$ applied to this Schur polynomial $s_{(3,2)}$ should yield the Schur polynomials $s_{(2,2)} + s_{(3,1)} + s_{(4,3)} + s_{(4,0)} + s_{(6,4)}$. Is this what you meant? |
May
29 |
asked | Symmetric powers of Schur polynomials |
May
24 |
awarded | Supporter |
May
24 |
accepted | Decomposition into irreducibles of symmetric powers of irreps. |
May
24 |
comment |
Decomposition into irreducibles of symmetric powers of irreps.
This is quite helpful as it gives me a new direction in which to read. I will look through Goodman-Wallach and continue with my study of Fulton and Harris. Thank you for your response Dr. Humphreys |
May
23 |
comment |
Decomposition into irreducibles of symmetric powers of irreps.
Hmmm, I am looking through his publications here: manchester.ac.uk/research/Roger.bryant/publications and he seems to treat with Lie algebras in characteristic $p$, but I should have mentioned that I am working over $\Bbb C$ here. And the symmetric powers he deals with are mostly with finite groups? Was there a particular paper you had in mind? Many thanks for your time. |
May
23 |
asked | Decomposition into irreducibles of symmetric powers of irreps. |
May
18 |
comment |
How to detect if a subgroup lands inside an orthogonal group?
@Aakumadula thank you. I will consult Fulton and Harris, I will surely find it in there |
May
18 |
asked | How to detect if a subgroup lands inside an orthogonal group? |
May
14 |
awarded | Scholar |
May
14 |
accepted | Finding spherical representations of $GL(n, \mathbb{C})$. |
May
14 |
comment |
Finding spherical representations of $GL(n, \mathbb{C})$.
Thanks for the information Marc, this is helpful |
May
14 |
comment |
Finding spherical representations of $GL(n, \mathbb{C})$.
@David that article is indeed interesting; however, I believe that my further edits will help to clarify exactly what I seek. Thank you for finding this though, and for those who do not have MathSciNet I have found a freely available version of the article here: eudml.org/doc/89398 in case a viewer of this question is indeed looking for the above classification. |
May
14 |
revised |
Finding spherical representations of $GL(n, \mathbb{C})$.
clarified the objective of the question |