The degenerate affine walled Brauer algebra

Abstract

We define a degenerate affine version of the walled Brauer algebra, that has the same role plaid by the degenerate affine Hecke algebra for the symmetric group algebra. We use it to prove a higher level mixed Schur-Weyl duality for gl_N. We consider then families of cyclotomic quotients of level two which appear naturally in Lie theory and we prove that they inherit from there a natural grading and a graded cellular structure.

References in corpus (4)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• A basis theorem for the affine oriented Brauer category and its cyclotomic quotients
• Affine and degenerate affine BMW algebras: The center
• Affine walled Brauer algebras

Cited by in corpus (5)

• A basis theorem for the affine oriented Brauer category and its cyclotomic quotients
• Cellular structures using ${\text{U}}_q$-tilting modules
• Supersymmetric polynomials and the center of the walled Brauer algebra
• Affine oriented Frobenius Brauer categories
• Cellular subalgebras of the partition algebra