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Showing 1 to 5 of 5 for “"semisimple Lie algebra"”.
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The fine structure of translation functors, the triangle function and a construction of R-matrices
… a simple finite-dimensional representation of a semisimple Lie algebra <br>with extremal weight <br>u and let e in E_{ <br>u} nonzero. <br>Let M( au) be the Verma module with highest weight au and v_{ au} the canonical <br>generator. <br>We investigate the projection of e otimes v_{ au} in E …
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On representations of quantum groups and Cherednik algebras
… thesis, we study quantum groups associated to a semisimple Lie algebra g. The classical Chevalley theorem states that for [ a Cartan subalgebra and W the Weyl group of g, the restriction of g-invariant polynomials on g to [ is an isomorphism onto the W-invariant polynomials on , Res: C[g]1 -+ …
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Rigid Analytic Quantum Groups
… of the quantized enveloping algebra of a semisimple Lie algebra $\mathfrak{g}$ and the quantized coordinate ring of the corresponding semisimple algebraic group $G$ respectively. We consider these to be quantum analogues of the Arens-Michael envelope of the enveloping algebra …
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Dual Pairs and Disconnected Reductive Groups
… invariant theory,” he introduces the notion of a Lie algebra dual pair (a pair (g₁, g₂) of reductive Lie subalgebras of a Lie algebra g such that g₁ and g₂ equal each other’s centralizers in g) and the notion of a Lie group dual pair (a pair (G₁, G₂) of reductive subgroups of a reductive Lie group …
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Der Kombinatorikfunktor V : graduierte Kategorie O, Hauptserien und primitive Ideale
… die uns eine graduierte Version von Hauptserien liefert. Deren Kombinatorik wird durch Elemente der Heckealgebra und Kazhdan-Lusztig-Polynome beschrieben. Mit Hilfe des von A. Joseph definierten Vervollständigungsfunktor werden Homomorphismen und Erweiterungen von Hauptserien bestimmt. Deren …