THE ANNIHILATOR OF TENSOR SPACE IN THE -ROOK MONOID ALGEBRA

DOI10.1017/S0004972716001404zbMath1475.20094OpenAlexW2594479019MaRDI QIDQ4975595

Zhan Kui Xiao

Publication date: 7 August 2017

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972716001404

zbMATH Keywords

Schur-Weyl dualitytensor space\(q\)-rook monoid

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08) Representation of semigroups; actions of semigroups on sets (20M30)

Cites Work

• Unnamed Item
• On tensor spaces for rook monoid algebras
• On tensor spaces for Birman-Murakami-Wenzl algebras
• The Brauer category and invariant theory
• Strongly multiplicity free modules for Lie algebras and quantum groups
• The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field
• The Iwahori algebra of \(\mathbf M_n(\mathbf F_q)\). A presentation and a representation on tensor space.
• Representations of the \(q\)-rook monoid.
• \(q\)-rook monoid algebras, Hecke algebras, and Schur-Weyl duality.
• Schur-Weyl reciprocity for Ariki-Koike algebras
• Representations of the rook monoid.
• Character formulas for \(q\)-rook monoid algebras
• Cellular algebras
• The second fundamental theorem of invariant theory for the orthogonal group.
• Cellular algebras and inverse semigroups.
• Representation theory of \(q\)-rook monoid algebras.
• Schur-Weyl reciprocity between quantum groups and Hecke algebras of type \(G(r,1,n)\)
• A Specht module analog for the rook monoid

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