The 0-rook monoid and its representation theory

zbMath1384.05171arXiv1910.11740MaRDI QIDQ1745109

Joël Gay, Florent Hivert

Publication date: 20 April 2018

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.11740

zbMATH Keywords

symmetric grouprook monoidIwahori Hecke algebrasrepresentation theory of monoids

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Hecke algebras and their representations (20C08)

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Partial Permutation and Alternating Sign Matrix Polytopes ⋮ Demazure product of permutations and hopping

Cites Work

• A tableau approach to the representation theory of 0-Hecke algebras
• 0-Hecke algebras of finite Coxeter groups.
• On the representation theory of finite \(J\)-trivial monoids
• The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field
• Algebraic structures on Grothendieck groups of a tower of algebras.
• Representation theory of the 0-Hecke algebra
• Noncommutative symmetric functions. IV: Quantum linear groups and Hecke algebras at \(q=0\)
• The Iwahori algebra of \(\mathbf M_n(\mathbf F_q)\). A presentation and a representation on tensor space.
• Representations of the \(q\)-rook monoid.
• Analogue of the Bruhat decomposition for algebraic monoids. II: The length function and the trichotomy
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