Mixed Schur-Weyl duality between general linear Lie algebras and cyclotomic walled Brauer algebras

2015/09/19 by Hebing Rui, Linliang Song, Rui, Hebing +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.1509.05855

36 pages

arxiv created 2015/09/19 · openalex publication_date 2015/09/19 · arxiv updated 2015/09/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Motivated by Brundan-Kleshchev's work on higher Schur-Weyl duality, we establish mixed Schur-Weyl duality between general linear Lie algebras and cyclotomic walled Brauer algebras in an arbitrary level. Using weakly cellular bases of cyclotomic walled Brauer algebras, we classify highest weight vectors of certain mixed tensor modules of general linear Lie algebras. This leads to an efficient way to compute decomposition matrices of cyclotomic walled Brauer algebras arising from mixed Schur-Weyl duality, which generalizes early results on level two walled Brauer algebras.

Citations

• Tensor Product Representations of General Linear Groups and Their Connections with Brauer Algebras
• Decomposition numbers of quantized walled Brauer algebras

Related

• Affine walled Brauer algebras
• Highest weight vectors of mixed tensor products of general linear Lie superalgebras
• Compact Schur-Weyl duality: real Lie groups and the cyclotomic Brauer algebra
• Walled Brauer algebras as idempotent truncations of level 2 cyclotomic quotients
• New versions of Schur-Weyl duality