The Berenstein-Kirillov group and cactus groups

DOI10.4171/JCA/36zbMath1446.05091arXiv1609.02046OpenAlexW3036292184MaRDI QIDQ2194415

Michael Chmutov, Max Glick, Pavlo Pylyavskyy

Publication date: 26 August 2020

Published in: Journal of Combinatorial Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.02046

zbMATH Keywords

cactus groupBender-Knuth involutionsBerenstein-Kirillov group

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Universal enveloping (super)algebras (17B35)

Related Items (9)

Shifted Bender-Knuth moves and a shifted Berenstein-Kirillov group ⋮ On Schützenberger modules of the cactus group ⋮ Cactus groups, twin groups, and right-angled Artin groups ⋮ Cyclic sieving for plane partitions and symmetry ⋮ Promotion, evacuation and cactus groups ⋮ Crystal structures for symmetric Grothendieck polynomials ⋮ Crystal structures for symmetric Grothendieck polynomials ⋮ Promotion on oscillating and alternating tableaux and rotation of matchings and permutations ⋮ Spectra of Bethe subalgebras of \(Y(\mathfrak{gl}_n)\) in tame representations

Cites Work

• Higher Bruhat orders connected with the symmetric group
• Rhombic tilings of polygons and classes of reduced words in Coxeter groups
• Fundamental groups of blow-ups.
• Cacti and cells
• Crystals and coboundary categories
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