Invariant tensors and the cyclic sieving phenomenon

zbMath1351.05231arXiv0912.1512MaRDI QIDQ727202

Bruce W. Westbury

Publication date: 6 December 2016

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.1512

zbMATH Keywords

cyclic sieving phenomenonpromotioncrystal graphs

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Simple, semisimple, reductive (super)algebras (17B20)

Related Items

Descent sets for symplectic groups ⋮ A marvellous embedding of the Lagrangian Grassmannian ⋮ Web bases for the general linear groups ⋮ Restriction of global bases and Rhoades's theorem ⋮ Promotion, evacuation and cactus groups ⋮ Minimal orbits of promotion ⋮ Crystals, semistandard tableaux and cyclic sieving phenomenon ⋮ Promotion on oscillating and alternating tableaux and rotation of matchings and permutations ⋮ \(q\)-dimensions of highest weight crystals and cyclic sieving phenomenon ⋮ Promotion of Kreweras words ⋮ Wronskians, cyclic group actions, and ribbon tableaux ⋮ Skew characters and cyclic sieving ⋮ Minuscule Doppelgängers, The Coincidental down-Degree Expectations Property, and Rowmotion

Uses Software

• Magma
• SageMath
• LiE
• OEIS

Cites Work

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• The canonical basis of the quantum adjoint representation
• Promotion and cyclic sieving via webs
• Enumeration of non-positive planar trivalent graphs
• Cyclic sieving, promotion, and representation theory
• Mirković-Vilonen cycles and polytopes.
• Generalisations of the Tits representation
• The crystal commutor and Drinfeld's unitarized \(R\)-matrix
• Quantum deformations of certain simple modules over enveloping algebras
• Coherence for compact closed categories
• The geometry of tensor calculus. I
• Hall algebras and quantum groups
• Based modules and good filtrations in algebraic groups
• Tortile tensor categories
• Canonical bases in tensor products and graphical calculus for \(U_ q(sl_ 2)\)
• The Magma algebra system. I: The user language
• The cyclic sieving phenomenon
• Crystal graphs and Young tableaux
• Paths and root operators in representation theory
• Spiders for rank 2 Lie algebras
• Cyclic sieving, rotation, and geometric representation theory
• Geometric Langlands duality and representations of algebraic groups over commutative rings
• Crystals and coboundary categories
• Crystalizing the q-analogue of universal enveloping algebras
• On algebras which are connected with the semisimple continuous groups
• WHAT IS...Cyclic Sieving?
• A pentagon of identities, graded tensor products and the Kirillov-Reshetikhin conjecture
• Beyond Kirillov-Reshetikhin modules
• Fonctions symétriques associées à des suites classiques de nombres
• The cyclic sieving phenomenon: a survey
• Canonical Bases Arising from Quantized Enveloping Algebras
• Braided and coboundary monoidal categories
• Canonical Bases Arising from Quantized Enveloping Algebras. II
• A uniform model for Kirillov-Reshetikhin crystals. Extended abstract
• Introduction to quantum groups