Schur-Weyl duality for the Brauer algebra and the ortho-symplectic Lie superalgebra

DOI10.1007/S00209-016-1669-YzbMath1393.17017arXiv1412.7853OpenAlexW2964193520WikidataQ115388751 ScholiaQ115388751MaRDI QIDQ330009

Catharina Stroppel, Michael Ehrig

Publication date: 24 October 2016

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.7853

zbMATH Keywords

Brauer algebraLie superalgebrainvariant theorySchur-Weyl duality

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Simple, semisimple, reductive (super)algebras (17B20) Lie algebras of linear algebraic groups (17B45) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)

Related Items (13)

Affine oriented Frobenius Brauer categories ⋮ Tensor ideals, Deligne categories and invariant theory ⋮ Invariants of the orthosymplectic Lie superalgebra and super Pfaffians ⋮ Cellular structures using \(U_q\)-tilting modules ⋮ SEMISIMPLICITY OF HECKE AND (WALLED) BRAUER ALGEBRAS ⋮ Tonal partition algebras: fundamental and geometrical aspects of representation theory ⋮ On the second fundamental theorem of invariant theory for the orthosymplectic supergroup ⋮ The split Casimir operator and solutions of the Yang-Baxter equation for the $osp(M|N)$ and $s\ell(M|N)$ Lie superalgebras, higher Casimir operators, and the Vogel parameters ⋮ Thick ideals in Deligne's category \(\underline{\mathrm{Re}}\mathrm{p}(O_\delta)\) ⋮ Walled Brauer algebras as idempotent truncations of level 2 cyclotomic quotients. ⋮ The affine VW supercategory ⋮ The blocks of the periplectic Brauer algebra in positive characteristic ⋮ On geometrically defined extensions of the Temperley-Lieb category in the Brauer category

Cites Work

• Gradings on walled Brauer algebras and Khovanov's arc algebra
• The first fundamental theorem of invariant theory for the orthosymplectic supergroup
• A basis theorem for the affine oriented Brauer category and its cyclotomic quotients
• On the structure of Brauer's centralizer algebras
• Centralizer algebras of the mixed tensor representations of quantum group \(U_ q(\text{gl}(n,\mathbb{C}))\)
• Tensor product representations of general linear groups and their connections with Brauer algebras
• Nazarov-Wenzl algebras, coideal subalgebras and categorified skew Howe duality
• The first fundamental theorem of invariant theory for the orthosymplectic super group
• Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras
• The second fundamental theorem of invariant theory for the orthogonal group.
• Brauer algebras and centralizer algebras for \(\text{SO}(2n,\mathbb{C})\)
• Khovanov's homology for tangles and cobordisms
• Invariants of the orthosymplectic Lie superalgebra and super Pfaffians
• A criterion on the semisimple Brauer algebras.
• Walled Brauer algebras as idempotent truncations of level 2 cyclotomic quotients.
• On algebras which are connected with the semisimple continuous groups
• Deligne’s category \underline{𝑅𝑒}𝑝(𝐺𝐿_{𝛿}) and representations of general linear supergroups
• Symmetry, Representations, and Invariants
• THE TENSOR ALGEBRA OF THE IDENTITY REPRESENTATION AS A MODULE OVER THE LIE SUPERALGEBRAS $ \mathfrak{Gl}(n,\,m)$ AND $ Q(n)$
• Koszul Gradings on Brauer Algebras
• SEMISIMPLICITY OF HECKE AND (WALLED) BRAUER ALGEBRAS
• The orthosymplectic superalgebra in harmonic analysis
• Serre presentations of Lie superalgebras
• Bernstein-Gel'fand-Gel'fand reciprocity and indecomposable projective modules for classical algebraic supergroups
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