Characters of Renner monoids and their Hecke algebras

DOI10.1142/S0218196720500514MaRDI QIDQ4970543

John M. O'Brien, Andrew Hardt, Alexander Vetter, Vaughan McDonald, Jared Marx-Kuo

Publication date: 14 October 2020

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.12343

zbMATH Keywords

Weyl grouprepresentationHecke algebracharacter tablesymplectic rook monoidRenner monoid

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Ordinary representations and characters (20C15) Representation theory for linear algebraic groups (20G05) Inverse semigroups (20M18) Representation of semigroups; actions of semigroups on sets (20M30) Algebraic monoids (20M32)

Cites Work

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• Generic Hecke algebra for Renner monoids.
• The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field
• Representations of the \(q\)-rook monoid.
• Linear algebraic monoids.
• Representations of the rook monoid.
• Character formulas for \(q\)-rook monoid algebras
• A Frobenius formula for the characters of Ariki-Koike algebras
• Hankel transform, Langlands functoriality and functional equation of automorphic \(L\)-functions
• Möbius functions and semigroup representation theory. II: Character formulas and multiplicities.
• REPRESENTATIONS OF THE SYMPLECTIC ROOK MONOID
• REPRESENTATIONS OF THE RENNER MONOID
• Sandwich Matrices, Solomon Algebras, and Kazhdan-Lusztig Polynomials
• Algebraic Monoids and Renner Monoids

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