Minuscule Elements of Weyl Groups, the Numbers Game, andd-Complete Posets
✍ Scribed by Robert A. Proctor
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 238 KB
- Volume
- 213
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
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 characterized by a collection of local structural properties, which form the definition of d-complete poset. In representation theoretic language, the top ''minuscule portions'' of weight diagrams for integrable representations of simply laced Kac᎐Moody algebras are shown to be distributive lattices. These lattices form a certain family of intervals of weak Bruhat orders. These Bruhat lattices are useful in studying reduced decompositions of -minuscule elements of Weyl groups and their associated Schubert varieties. The d-complete posets have recently been proven to possess both the hook length and the jeu de taquin properties.