A bijection on core partitions and a parabolic quotient of the affine symmetric group

DOI10.1016/j.jcta.2009.03.013zbMath1183.05089arXiv0804.1380OpenAlexW2035013951MaRDI QIDQ1040847

Monica Vazirani, Chris Berg, Brant C. Jones

Publication date: 26 November 2009

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.1380

zbMATH Keywords

core partitionaffine root systembeta numberparabolic quotientAbacusminimal length coset representative

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30)

Related Items (11)

Advances in the Theory of Cores and Simultaneous Core Partitions ⋮ The Corners of Core Partitions ⋮ Abacus models for parabolic quotients of affine Weyl groups ⋮ Counting Shi regions with a fixed separating wall ⋮ A core model for \(G_2\) ⋮ The enumeration of fully commutative affine permutations ⋮ A bijection between dominant Shi regions and core partitions ⋮ Bijections between generalized Catalan families of types \(A\) and \(C\) ⋮ Core partitions and block coverings ⋮ Fixed points in smooth Calogero-Moser spaces ⋮ Bijective projections on parabolic quotients of affine Weyl groups

Cites Work

• \((\ell,0)\)-Carter partitions, their crystal-theoretic behavior and generating function
• Blocks for symmetric groups and their covering groups and quadratic forms
• Tableaux on \(k+1\)-cores, reduced words for affine permutations, and \(k\)-Schur expansions
• Cranks and t-cores
• Crystal base for the basic representation of \(U_ q({\mathfrak sl}^\wedge (n))\)
• Combinatorics of Coxeter Groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A bijection on core partitions and a parabolic quotient of the affine symmetric group