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Results tagged with rt.representation-theory
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user 147236
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
1
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Number of representations of a given dimension
Let $G$ be a (semi)simple algebraic group over $\mathbb C$ and let $d \in \mathbb Z_{>0}$ a fixed integer.
Let us suppose that there is an irreducible $G$-representation $V$ such that $\dim V=d$. Can …
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2
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1
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Do representations of same dimension implies isomorphic closed orbits?
Let us recall this fact. Let $G$ be a semisimple algebraic group over $\mathbb C$ and let $V,V'$ be two irreducible $G$-representations. We denote by $X,X'$ the unique closed $G$-orbits contained in $ …
- 381
2
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1
answer
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Irreducible $G$-representations with unital algebra structure
Let us work over $\mathbb C$. Suppose that $G$ is a semisimple algebraic group and let $H \subset G$ be a maximal torus. Consider a dominant weight $\omega$, then one can associate a unique irreducibl …
- 381
1
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0
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Global sections of a vector bundle over $OG(2,7)$
Let us work over $\mathbb C$, using the Grothendieck projectivization $\mathbb P():=Proj(Sym())$.
Consider a $7$-dimensional vector space $V$ endowed with a symmetric non-degenerate bilinear form $q:V …
- 381