“Whoa! It's like Spotify but for academic articles.”

Instant Access to Thousands of Journals for just $40/month

Get 2 Weeks Free

Faces of Weight Polytopes and a Generalization of a Theorem of Vinberg

The paper is motivated by the study of graded representations of Takiff algebras, cominuscule parabolics, and their generalizations. We study certain special subsets of the set of weights (and of their convex hull) of the generalized Verma modules (or GVM’s) of a semisimple Lie algebra $\mathfrak{g}$ . In particular, we extend a result of Vinberg and classify the faces of the convex hull of the weights of a GVM. When the GVM is finite-dimensional, we answer a natural question that arises out of Vinberg’s result: when are two faces the same? We also extend the notion of interiors and faces to an arbitrary subfield $\mathbb{F}$ of the real numbers, and introduce the idea of a weak $\mathbb{F}$ –face of any subset of Euclidean space. We classify the weak $\mathbb{F}$ –faces of all lattice polytopes, as well as of the set of lattice points in them. We show that a weak $\mathbb{F}$ –face of the weights of a finite-dimensional $\mathfrak{g} $ –module is precisely the set of weights lying on a face of the convex hull. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebras and Representation Theory Springer Journals

Loading next page...

You're reading a free preview. Subscribe to read the entire article.

And millions more from thousands of peer-reviewed journals, for just $40/month

Get 2 Weeks Free

To be the best researcher, you need access to the best research

  • With DeepDyve, you can stop worrying about how much articles cost, or if it's too much hassle to order — it's all at your fingertips. Your research is important and deserves the top content.
  • Read from thousands of the leading scholarly journals from Springer, Elsevier, Nature, IEEE, Wiley-Blackwell and more.
  • All the latest content is available, no embargo periods.

Stop missing out on the latest updates in your field

  • We’ll send you automatic email updates on the keywords and journals you tell us are most important to you.
  • There is a lot of content out there, so we help you sift through it and stay organized.