# Characters of highest weight modules and integrability

@article{Dhillon2016CharactersOH, title={Characters of highest weight modules and integrability}, author={Gurbir Singh Dhillon and Apoorva Khare}, journal={arXiv: Representation Theory}, year={2016} }

We give positive formulas for the weights of every simple highest weight module $L(\lambda)$ over an arbitrary Kac-Moody algebra. Under a mild condition on the highest weight, we express the weights of $L(\lambda)$ as an alternating sum similar to the Weyl-Kac character formula. For general highest weight modules, we answer questions of Bump and Lepowsky on weights, and a question of Brion on the corresponding $D$-modules. Many of these results are new even in finite type. We prove similar… Expand

#### 5 Citations

Faces of highest weight modules and the universal Weyl polyhedron

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- 2017

Abstract Let V be a highest weight module over a Kac–Moody algebra g , and let conv V denote the convex hull of its weights. We determine the combinatorial isomorphism type of conv V, i.e. we… Expand

The Weyl-Kac weight formula

- Mathematics
- 2018

We provide the first formulae for the weights of all simple highest weight modules over Kac-Moody algebras. For generic highest weights, we present a formula for the weights of simple modules similar… Expand

Demazure formula for An Weyl polytope sums

- Mathematics, Physics
- Journal of Mathematical Physics
- 2021

The weights of finite-dimensional representations of simple Lie algebras are naturally associated with Weyl polytopes. Representation characters decompose into multiplicity-free sums over the weights… Expand

Demazure Formulas for Weight Polytopes

- Physics, Mathematics
- 2020

The characters of simple Lie algebras are naturally decomposed into lattice polytope sums. The Brion formula for those polytope sums is remarkably similar to the Weyl character formula. Here we start… Expand

Moving between weights of weight modules

- Mathematics
- 2020

In Lie theory the partial sum property (PSP) says that for a root system in any Kac-Moody algebra, every positive root is an ordered sum of simple roots whose partial sums are all roots. In this… Expand

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