The Iwahori algebra of \(\mathbf M_n(\mathbf F_q)\). A presentation and a representation on tensor space.
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Publication:1427385
DOI10.1016/j.jalgebra.2003.08.013zbMath1155.20300OpenAlexW2068663543MaRDI QIDQ1427385
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
Hecke algebrasdefining relationsupper triangular matricesreductive monoidsIwahori algebrasalgebra generatorsdeformed versions of Coxeter presentations
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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