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@misc{MBWWM,
      TITLE = {Moving between weights of weight modules}, 
      author={G.K.~Teja},
      year={2021},
      eprint={2012.07775},
      archivePrefix={arXiv},
      primaryClass={math.RT}
}
@misc{WFHMRS,
      title={Weak faces of highest weight modules and root systems}, 
      author={G.K.~Teja},
      year={2021},
      eprint={2106.14929},
      archivePrefix={arXiv},
      primaryClass={math.RT}
}

@article{KhareJ.Alg,
author = {A.~Khare},
title = {Faces and maximizer subsets of highest weight modules},
journal = {J.~Algebra},
volume = {455},
pages = {32--76},
year = {2016},
}
%doi = {10.1016/j.jalgebra.2016.02.004}
%url = {https://www.sciencedirect.com/science/article/pii/S0021869316000934},

@article{KhareAdv,
title = {Faces of highest weight modules and the universal Weyl polyhedron},
author = {G.~Dhillon and A.~Khare},
journal = {Adv. Math.},
volume = {319},
pages = {111--152},
year = {2017},
}

@article{Chari-Greenstein,
  title = {A family of Koszul algebras arising from finite-dimensional representations of simple Lie algebras},
  author = {V.~Chari and J.~Greenstein},
  journal = {Adv. Math.},
  volume = {220},
  pages = {1193--1221},
    year = {2009}
}

@article{Satake,
 author = {I.~Satake},
 journal = {Ann. of Math.},
 number = {1},
 pages = {77--110},
 title = {On representations and compactifications of symmetric
 Riemannian spaces},
 volume = {71},
 year = {1960}
}
 %URL = {http://www.jstor.org/stable/1969880},
 %publisher = {Annals of Mathematics},

@article{Ridenour,
author = {A. Khare and T. Ridenour},
title = {Faces of weight polytopes and a generalization of a theorem of Vinberg},
journal = {Algebr. Represent. Theory},
volume = {15},
pages ={593--611},
year = {2012}, 
}



@book{Kac,
place={Cambridge},
edition={3},
title={Infinite-Dimensional Lie Algebras},
publisher={Cambridge Univ.\ Press},
author={Kac, V.G.},
year={1990}
}

@article{Borel,
  title={Groupes r{\'e}ductifs},
  author={A.~Borel and J.~Tits},
  journal={Publ. Math. Inst. Hautes Etudes Sci.},
  year={1965},
  volume={27},
  pages={55--150}
}

@ARTICLE{Vinberg,
       author = {{Vinberg}, {\`E}.B.},
        title = "{On certain commutative subalgebras of a universal
	enveloping algebra}",
      journal = {Izvestiya: Math.},
         year = {1991},
       volume = {36},
       number = {1},
        pages = {1--22},
      }
          %doi = {10.1070/IM1991v036n01ABEH001925}
       %adsurl = {https://ui.adsabs.harvard.edu/abs/1991IzMat..36....1V},
      %adsnote = {Provided by the SAO/NASA Astrophysics Data System}



@article{ Dolbin,
title = {Ideals in parabolic subalgebras of simple Lie algebras},
author = {V.~Chari and {R.J.~Dolbin} and T.~Ridenour},
journal = {Contemp.\ Math.},
volume = {490},
year = {2009}, 
pages = {47--60}
}
 
@Book{ Humphreys,
author = {J.E.~Humphreys},
title = {Introduction to Lie Algebras and Representation Theory},
publisher = { Springer, NY},
year = { 1972 },
}