Cyclic sieving of finite Grassmannians and flag varieties

Andrew Berget; Jia Huang

doi:10.1016/j.disc.2011.10.015

Cyclic sieving of finite Grassmannians and flag varieties

Andrew Berget, Jia Huang

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we prove instances of the cyclic sieving phenomenon for finite Grassmannians and partial flag varieties, which carry the action of various tori in the finite general linear group GL _n(double-struck F sign _q). The polynomials involved are sums of certain weights of the minimal length parabolic coset representatives of the symmetric group fraktur S sign _n, where the weight of a coset representative can be written as a product over its inversions.

Original language	English (US)
Pages (from-to)	898-910
Number of pages	13
Journal	Discrete Mathematics
Volume	312
Issue number	5
DOIs	https://doi.org/10.1016/j.disc.2011.10.015
State	Published - Mar 6 2012
Externally published	Yes

Keywords

Cyclic sieving
Finite field
Flag variety
Grassmannian

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2011.10.015

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abstract = "In this paper, we prove instances of the cyclic sieving phenomenon for finite Grassmannians and partial flag varieties, which carry the action of various tori in the finite general linear group GL n(double-struck F sign q). The polynomials involved are sums of certain weights of the minimal length parabolic coset representatives of the symmetric group fraktur S sign n, where the weight of a coset representative can be written as a product over its inversions.",

keywords = "Cyclic sieving, Finite field, Flag variety, Grassmannian",

author = "Andrew Berget and Jia Huang",

note = "Funding Information: The authors would like to thank Julian Gold for preliminary computations done during a summer 2010 REU at UC Davis with the first author. They also thank Victor Reiner and Dennis Stanton for helpful comments and suggestions. Berget was partially supported by NSF grant DMS-0636297 . Huang was partially supported by NSF grant DMS-1001933 . ",

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AU - Huang, Jia

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AB - In this paper, we prove instances of the cyclic sieving phenomenon for finite Grassmannians and partial flag varieties, which carry the action of various tori in the finite general linear group GL n(double-struck F sign q). The polynomials involved are sums of certain weights of the minimal length parabolic coset representatives of the symmetric group fraktur S sign n, where the weight of a coset representative can be written as a product over its inversions.

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KW - Finite field

KW - Flag variety

KW - Grassmannian

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Cyclic sieving of finite Grassmannians and flag varieties

Abstract

Keywords

ASJC Scopus subject areas

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