# Minuscule elements of Weyl groups

@article{Stembridge2001MinusculeEO, title={Minuscule elements of Weyl groups}, author={John R. Stembridge}, journal={Journal of Algebra}, year={2001}, volume={235}, pages={722-743} }

Abstract We provide several characterizations of the “λ-minuscule” elements of Weyl groups studied by D. Peterson and R. A. Proctor and extend Proctor's classification from the simply-laced case to the general case.

## Figures from this paper

## 84 Citations

Enumeration for strong minuscule elements in the Weyl group of type A

- Mathematics
- 2019

In the case of finite-dimensional simple Lie algebra of type A, we enumerate special classes of pre-dominant integral weights and dominant minuscule elements. In addition, as an application, we give…

On dominance and minuscule Weyl group elements

- Mathematics
- 2009

Fix a Dynkin graph and let λ be a coweight. When does there exist an element w of the corresponding Weyl group such that w is λ-minuscule and w(λ) is dominant? We answer this question for general…

Cyclotomic quiver Hecke algebras corresponding to minuscule representations

- Mathematics
- 2019

In the paper, we give an explicit basis of the cyclotomic quiver Hecke algebra corresponding to a minuscule representation of finite type.

Perfect Codes for Generalized Deletions from Minuscule Elements of Weyl Groups

- Computer ScienceArXiv
- 2018

This paper discusses a connection between insertion/deletion (ID) codes and minuscule elements of Weyl groups.

Some combinatorial aspects of generalised Bott-Samelson varieties.

- Mathematics
- 2019

We obtain two combinatorial results: an equality of Weyl groups and an inequality of roots, in the setting of generalised Bott-Samelson resolutions of minuscule Schubert varieties. These results are…

Homogeneous representations of Khovanov-Lauda algebras

- Mathematics
- 2008

We construct irreducible graded representations of simply laced Khovanov�Lauda algebras which are concentrated in one degree. The underlying combinatorics of skew shapes and standard tableaux…

Minimal rational curves on generalized Bott–Samelson varieties

- MathematicsCompositio Mathematica
- 2021

We investigate families of minimal rational curves on Schubert varieties, their Bott–Samelson desingularizations, and their generalizations constructed by Nicolas Perrin in the minuscule case. In…

Combinatorics of Minuscule Representations

- Mathematics
- 2013

Introduction 1. Classical Lie algebras and Weyl groups 2. Heaps over graphs 3. Weyl group actions 4. Lie theory 5. Minuscule representations 6. Full heaps over affine Dynkin diagrams 7. Chevalley…

Towards a Littlewood-Richardson rule for Kac-Moody homogeneous spaces

- Mathematics
- 2009

We prove a general combinatorial formula yielding the intersection number $c_{u,v}^w$ of three particular $\Lambda$-minuscule Schubert classes in any Kac-Moody homogeneous space, generalising the…

On a conjecture of Kottwitz and Rapoport

- Mathematics
- 2008

We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur's Inequality for all split and quasi-split (connected) reductive groups. These results are related to the…

## References

SHOWING 1-10 OF 14 REFERENCES

Quasi-Minuscule Quotients and Reduced Words for Reflections

- Mathematics
- 2001

We study the reduced expressions for reflections in Coxeter groups, with particular emphasis on finite Weyl groups. For example, the number of reduced expressions for any reflection can be expressed…

Nilpotent Orbits and Commutative Elements

- Mathematics
- 1997

Abstract Let W be a simply laced Coxeter group with generating set S , and let W c denote the subset consisting of those elements whose reduced expressions have no substrings of the form sts for any…

Dynkin Diagram Classification of λ-Minuscule Bruhat Lattices and of d-Complete Posets

- Mathematics
- 1999

Abstractd-Complete posets are defined to be posets which satisfy certain local structural conditions. These posets play or conjecturally play several roles in algebraic combinatorics related to the…

Minuscule Elements of Weyl Groups, the Numbers Game, andd-Complete Posets

- Mathematics
- 1999

Abstract Certain posets associated to a restricted version of the numbers game of Mozes are shown to be distributive lattices. The posets of join irreducibles of these distributive lattices are…

Reflection Groups and Coxeter Groups

- Mathematics
- 2003

This chapter is of an auxiliary nature and contains the modicum of the theory of finite reflection groups and Coxeter groups which we need for a systematic development of the theory of Coxeter…

On the Fully Commutative Elements of Coxeter Groups

- Mathematics
- 1996

Let W be a Coxeter group. We define an element w ∈ W to be fully commutative if any reduced expression for w can be obtained from any other by means of braid relations that only involve commuting…

Groupes et algèbres de Lie

- Philosophy
- 1971

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…

[Effect of BN52021 on platelet activating factor induced aggregation of psoriatic polymorphonuclear neutrophils].

- MedicineZhonghua yi xue za zhi
- 1994

It is suggested that PAF and PMN play an important pathophysiological role in the development of psoriasis, and application of PAF antagonists may be a new and effective approach to the management of Psoriasis.