Boolean intersection ideals of permutations in the Bruhat order

Tenner, Bridget Eileen

doi:10.54550/eca2022v2s3r23

Search citation statements

Order By: Relevance

Paper Sections

Select...

Optimal Ranks1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to investigate this kind of guess, we need a better understanding of the combinatorial structure of intersections of principal Bruhat ideals. Maybe the recent preprints [4,32], which appeared after the preprint version of the present paper, will be helpful.…”

Section: Optimal Ranksmentioning

confidence: 99%

Intersecting principal Bruhat ideals and grades of simple modules

Mazorchuk¹,

Tenner²

2022

Combinatorial Theory

View full text Add to dashboard Cite

We prove that the grades of simple modules indexed by boolean permutations, over the incidence algebra of the symmetric group with respect to the Bruhat order, are given by Lusztig's a-function. Our arguments are combinatorial, and include a description of the intersection of two principal order ideals when at least one permutation is boolean. An important object in our work is a reduced word written as minimally many runs of consecutive integers, and one step of our argument shows that this minimal quantity is equal to the length of the second row in the permutation's shape under the Robinson-Schensted correspondence. We also prove that a simple module over the above-mentioned incidence algebra is perfect if and only if its index is the longest element of a parabolic subgroup.

show abstract

Section: Optimal Ranksmentioning

confidence: 99%