THE PARTIAL ORDER OF DOMINANT WEIGHTS

@article{Stembridge1998THEPO,
  title={THE PARTIAL ORDER OF DOMINANT WEIGHTS},
  author={John R. Stembridge},
  journal={Advances in Mathematics},
  year={1998},
  volume={136},
  pages={340-364}
}
  • J. Stembridge
  • Published 25 June 1998
  • Mathematics
  • Advances in Mathematics
Abstract The weight lattice of a crystallographic root system is partially ordered by the rule that λ > μ if λ − μ is a nonnegative integer linear combination of positive roots. In this paper, we study the subposet formed by the dominant weights. In particular, we prove that λ covers μ in this partial order only if λ − μ belongs to a distinguished subset of the positive roots. Also, if the root system is irreducible, we prove that the Mobius function of the partial order takes on only the… 

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References

SHOWING 1-10 OF 11 REFERENCES

The lattice of integer partitions

A Class of Lattices with Möbius Function ± 1, 0

  • C. Greene
  • Mathematics, Computer Science
    Eur. J. Comb.
  • 1988

What Is Enumerative Combinatorics

The basic problem of enumerative combinatorics is that of counting the number of elements of a finite set. Usually are given an infinite class of finite sets S i where i ranges over some index set I

Introduction to Lie Algebras and Representation Theory

Preface.- Basic Concepts.- Semisimple Lie Algebras.- Root Systems.- Isomorphism and Conjugacy Theorems.- Existence Theorem.- Representation Theory.- Chevalley Algebras and Groups.- References.-

Groupes et algèbres de Lie

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements. Ce premier volume du Livre sur

The lattice of integer partitions, Discrete Math

  • The lattice of integer partitions, Discrete Math
  • 1973

A class of lattices with MM obius function 1

  • Europ. J. Combin
  • 1988

\Groupes et Alg ebres de Lie

  • \Groupes et Alg ebres de Lie
  • 1981

A Maple package for root systems and nite Coxeter groups, manuscript

  • A Maple package for root systems and nite Coxeter groups, manuscript
  • 1997