@prefix dcat: . @prefix dct: . @prefix foaf: . @prefix vcard: . @prefix xsd: . a dcat:Dataset ; dct:description """ Let $V$ be a finite dimensional complex vector space.
A subset $X$ in $V$ has the separation property if
the following holds: For any pair $l$, $m$ of linearly
independent linear functions on $V$ there is a point $x$
in $X$ such that $l(x)=0$ and $m(x)$ is nonzero. We study the
the case where $V=\\C[x,y]_n$ is an irreducible representation
of $\\SL_2$. The subsets we are interested in
are the closures of $\\SL_2$-orbits $O_f$ of forms in
$\\C[x,y]_n$.
We give an explicit description of those orbits that have
the separation property:

The closure of $O_f$ has the separation property if and
only if the form $f$ contains a linear factor of
multiplicity one.

In the second part of this thesis we study
tensor products $V_{\\lambda}\\otimes V_{\\mu}$
of irreducible $G$-representations (where
$G$ is a reductive complex algebraic group).
In general, such a tensor product is not irreducible
anymore.
It is a fundamental question how the irreducible
components are embedded in the tensor product.
A special component of the tensor product is the
so-called Cartan component $V_{\\lambda+\\mu}$
which is the component with the maximal highest weight.
It appears exactly once in the decomposition.

Another interesting subset of $V_{\\lambda}\\otimes V_{\\mu}$
is the set of decomposable tensors. The following
question arises in this context:

Is the set of decomposable tensors in the Cartan
component of such a tensor product given as the closure
of the $G$--orbit of a highest weight vector?

If this is the case we say that the Cartan component is
{\\it small}.
We show that in general, Cartan components are small.
We present what happens for $G=\\SL_2$ and $G=\\SL_3$ and
discuss the representations of the special linear group
in detail. """ ; dct:identifier "tel-00012189" ; dct:issued "2026-05-28T09:59:17.024661"^^xsd:dateTime ; dct:language "fr" ; dct:modified "2026-05-28T09:59:17.024667"^^xsd:dateTime ; dct:publisher ; dct:title "Two contributions to the representation theory of algebraic groups" ; dcat:contactPoint [ a vcard:Organization ; vcard:fn "CCSD" ] ; dcat:distribution ; dcat:keyword "infoeu-reposemanticsdoctoralthesis", "mathmathematics-math", "propriete-de-separation", "representation-theory-of-algebraic-groups", "separation-property", "theorie-de-representations-de-groupes-algebriques", "theses" ; dcat:landingPage . a dcat:Distribution ; dct:format "HTML" ; dct:issued "2026-05-28T09:59:17.047722"^^xsd:dateTime ; dct:modified "2026-05-28T09:59:16.991338"^^xsd:dateTime ; dct:title "Two contributions to the representation theory of algebraic groups" ; dcat:accessURL . a foaf:Agent ; foaf:name "test_moissonnage_selune" . a foaf:Document .