A third look at weight diagrams

Nikolai Vavilov

Displaying similar documents to “A third look at weight diagrams”

A character approach to Looijenga's invariant theory for generalized root systems

Peter Slodowy (1985)

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An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties

Hans Plesner Jakobsen (1996)

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Commutativity of intertwining operators for semisimple groups

A. W. Knapp (1982)

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Tight quotients and double quotients in the Bruhat order.

Stembridge, John R. (2004)

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Generalized Verma module homomorphisms in singular character

Peter Franek (2006)

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In this paper we study invariant differential operators on manifolds with a given parabolic structure. The model for the parabolic geometry is the quotient of the orthogonal group by a maximal parabolic subgroup corresponding to crossing of the $k$ -th simple root of the Dynkin diagram. In particular, invariant differential operators discussed in the paper correspond (in a flat model) to the Dirac operator in several variables.

On normal abelian subgroups in parabolic groups

Gerhard Röhrle (1998)

Annales de l'institut Fourier

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Let $G$ be a reductive algebraic group, $P$ a parabolic subgroup of $G$ with unipotent radical $P_{u}$ , and $A$ a closed connected subgroup of $P_{u}$ which is normalized by $P$ . We show that $P$ acts on $A$ with finitely many orbits provided $A$ is abelian. This generalizes a well-known finiteness result, namely the case when $A$ is central in $P_{u}$ . We also obtain an analogous result for the adjoint action of $P$ on invariant linear subspaces of the Lie algebra of $P_{u}$ which are abelian Lie algebras. Finally, we discuss...