Minimal length elements in some double cosets of Coxeter groups

By Xuhua He. 2006

86 citations recorded by the source corpus.

Abstract We study the minimal length elements in some double cosets of Coxeter groups and use them to study Lusztig's G-stable pieces and the generalization of G-stable pieces introduced by Lu and Yakimov. We also use them to study the minimal length elements in a conjugacy class of a finite Coxeter group and prove a conjecture in [M. Geck, S. Kim, G. Pfeiffer, Minimal length elements in twisted conjugacy classes of finite Coxeter groups, J. Algebra 229 (2) (2000) 570–600].

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0e42a6a4b448a19c3f175eb3132aca364169bc4e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Michael Rapoport
2. S. Nie
3. Pavel Galashin
4. Steven N. Karp
5. Thomas Lam

In Discrete Mathematics and Combinatorics

1. S. Nie
2. Pavel Galashin
3. Michael Rapoport
4. Steven N. Karp
5. Xuhua He
6. Thomas Lam
7. Mark Shimozono
8. Jennifer Morse

In Geometry and Topology

1. Xuhua He
2. S. Nie
3. Michael Rapoport
4. Pavel Galashin
5. Steven N. Karp
6. Thomas Lam
7. E. Viehmann
8. Georgios Pappas

Citations in the corpus

• GEOMETRIC AND HOMOLOGICAL PROPERTIES OF AFFINE DELIGNE-LUSZTIG VARIETIES (2012, methodology): “This is achieved by combining the “dimension=degree” theorem with the partial conjugation method developed in [13] and the dimension formula for affine Deligne-Lusztig varieties in the affine Grassmannian in [7] and [31].”
• Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties (2014, methodology): “1), proved by the “partial conjugation method” in [8].”
• Minimal length elements of extended affine Weyl groups (2011, methodology): “Property (1) was due to Geck and Pfeiffer [9] and the first author [11].”
• Regularity theorem for totally nonnegative flag varieties (2019, methodology): “We formulate our results in the abstract language of totally nonnegative spaces since we expect that they can be applied in other contexts, such as to totally nonnegative Kac– Moody flag varieties, totally nonnegative double Bruhat cells [8], spaces of electrical networks [23], spaces of boundary co”
• Stratifications in the reduction of Shimura varieties (2015, methodology): “The proof uses the “partial conjugation method” of [16].”