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Results tagged with rt.representation-theory
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user 14009
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
1
vote
1
answer
645
views
Tensor product decomposition of V and g
Let $g$ be a simple complex Lie algebra with an irreducible representation $g\subset so(V)$ with the highest weight $\Lambda$.
In the book by Onishchik and Vinberg "Lie groups and algebraic
groups" t …
- 59
4
votes
0
answers
174
views
Number of submodules in $\wedge^2 V$ and $S^2V$ isomorphic to $\mathfrak{g}$
Let $\mathfrak{g}$ be a simple complex Lie algebra. Let
$\mathfrak{g}\subset\mathfrak{so}(V)$ be an orthogonal
irreducible representation. It can be shown that the number of
$\mathfrak{g}$-submodule …
- 59
1
vote
1
answer
420
views
A subalgebra of the Virasoro algebra
Let $L_n$ ($n\in\mathbb{Z}$) and $c$ be the standard generators of the Virasoro algebra ${\rm Vit}$. In the literature one usually considers the involutive authomorphism given by $\tau(L_n)=-L_{-n}$, …
- 59