Representations of Brauer category and categorification

DOI10.1016/j.jalgebra.2020.04.013zbMath1459.17044OpenAlexW3016432868MaRDI QIDQ2178552

Hebing Rui, Linliang Song

Publication date: 11 May 2020

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2020.04.013

zbMATH Keywords

Brauer algebrahighest weight categorystandard modulescategorificationcostandard modulesBrauer categoryextended affine special linear algebrastratified category

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Grothendieck groups, (K)-theory, etc. (16E20) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Associative rings and algebras arising under various constructions (16S99) Categorification (18N25)

Related Items

A basis theorem for the affine Kauffman category and its cyclotomic quotients, Blocks of the Brauer category over the complex field, Semi-Infinite Highest Weight Categories, Representations of weakly triangular categories, The representation theory of Brauer categories. I: triangular categories

Cites Work

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• Thick ideals in Deligne's category \(\underline{\mathrm{Re}}\mathrm{p}(O_\delta)\)
• Diagrammatic Kazhdan-Lusztig theory for the (walled) Brauer algebra.
• Decomposition matrices of Birman-Murakami-Wenzl algebras
• The Brauer category and invariant theory
• On the structure of Brauer's centralizer algebras
• On automorphisms of Kac-Moody algebras and groups
• On the semisimplicity of the Brauer centralizer algebras
• On the decomposition numbers of the Hecke algebra of \(G(m,1,n)\)
• Quantum symmetric pairs and their zonal spherical functions.
• Categorification of quantum symmetric pairs. I
• Borelic pairs for stratified algebras
• Cellular algebras
• Affine Brauer category and parabolic category \(\mathcal{O}\) in types \(B, C, D\)
• Specht modules and semisimplicity criteria for Brauer and Birman-Murakami-Wenzl algebras.
• A criterion on the semisimple Brauer algebras.
• The blocks of the Brauer algebra in characteristic zero
• Character formulas for tilting modules over Kac-Moody algebras
• Koszul Gradings on Brauer Algebras
• Kazhdan-Lusztig theory of super type D and quantum symmetric pairs
• A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
• Cyclotomic Nazarov-Wenzl Algebras
• Quantum invariants of knots and 3-manifolds