The Iwahori algebra of \(\mathbf M_n(\mathbf F_q)\). A presentation and a representation on tensor space.

DOI10.1016/j.jalgebra.2003.08.013zbMath1155.20300OpenAlexW2068663543MaRDI QIDQ1427385

Louis Solomon

Publication date: 14 March 2004

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2003.08.013

zbMATH Keywords

Hecke algebrasdefining relationsupper triangular matricesreductive monoidsIwahori algebrasalgebra generatorsdeformed versions of Coxeter presentations

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Semigroups of transformations, relations, partitions, etc. (20M20)

Related Items (8)

Motzkin algebras ⋮ Representations of the \(q\)-rook monoid. ⋮ Generic Hecke algebra for Renner monoids. ⋮ The 0-rook monoid and its representation theory ⋮ Representation theory of \(q\)-rook monoid algebras. ⋮ Jucys–Murphy elements of partition algebras for the rook monoid ⋮ PRESENTATION FOR RENNER MONOIDS ⋮ THE ANNIHILATOR OF TENSOR SPACE IN THE -ROOK MONOID ALGEBRA

Cites Work

• The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field
• Analogue of the Bruhat decomposition for algebraic monoids
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• A Frobenius formula for the characters of the Hecke algebras
• Representations of the \(q\)-rook monoid.
• \(q\)-rook monoid algebras, Hecke algebras, and Schur-Weyl duality.
• Representations of the rook monoid.
• Character formulas for \(q\)-rook monoid algebras
• Monoid Hecke algebras
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