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Results tagged with rt.representation-theory
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user 32389
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
3
votes
Representation theory, classical Lie algebra, D_{n}
Maybe the following article will be helpful: http://arxiv.org/abs/math/9902060 (A. I. Molev, A weight basis for representations of even orthogonal Lie algebras).
For a quick and elementary introducti …
- 16.5k
8
votes
ADE type Dynkin diagrams
This paper http://arxiv.org/abs/hep-th/0006151 (CFT, BCFT, ADE and all that, by Jean-Bernard Zuber) provides the following list of mathematical objects that fall in an ADE classification:
simple si …
- 16.5k
3
votes
Appropriate Recursion relations for Wigner 3j Symbols
Try these references http://scitation.aip.org/content/aip/journal/jmp/16/10/10.1063/1.522426?ver=pdfcov (Exact recursive evaluation of 3j‐ and 6j‐coefficients for quantum‐mechanical coupling of angula …
- 16.5k
4
votes
Accepted
tensor product of massless Poincare representations
I think the answer is given in the paper https://aip.scitation.org/doi/10.1063/1.1703659 (Decomposition of Direct Products of Representations of the Inhomogeneous Lorentz Group, by J. S. Lomont).
- 16.5k
8
votes
List of Casimir elements of low dimensional Lie algebras
A more general problem (finding all invariant functions of the group generators for all real Lie algebras of dimension up to five) was considered in Invariants of real low dimension Lie algebras by J. …
- 16.5k
2
votes
Resource for learning quantum mechanics from the viewpoint of representation theory
Basic foundations of quantum mechanics in a representation theoretic language can be found in van den Ban's lectures "Applications of representation theory in classical quantum mechanics" at this page …
14
votes
How to make the Capelli's identity less mysterious?
This order of terms in the determinant is the most mysterious point for me. Is there any reason for it? What happens if one chooses some other ordering of terms: will the Capelli identity be modifi …
- 16.5k
4
votes
Accepted
Closed form for 3j-symbol ratios
The following recursion relation
$$
C(m_2+1,m_3-1)\begin{pmatrix}l_1 &l_2 &l_3\\m_1&m_2+1&m_3-1\end{pmatrix}+
D(m_2,m_3)\begin{pmatrix}l_1 &l_2 &l_3\\m_1&m_2&m_3\end{pmatrix}+$$ $$
C(m_2,m_3)\begin{p …
- 16.5k
1
vote
Branching from $E(6)$ to $SO(10) \times U(1)$
Maybe the following reference will be useful: https://www.sciencedirect.com/science/article/pii/0370157381900922 (Group theory for unified model building, by R.Slansky).
- 16.5k
4
votes
Accepted
Young tableaux for exceptional Lie algebras
Young diagrams for the exceptional Lie algebras are considered in the book https://press.princeton.edu/titles/8839.html (Group Theory: Birdtracks, Lie's, and Exceptional Groups, by Predrag Cvitanovic) …
- 16.5k