The degenerate affine walled Brauer algebra

TL;DR

This paper introduces a degenerate affine walled Brauer algebra, establishing its role in higher level Schur-Weyl duality for gl_N and exploring cyclotomic quotients with graded cellular structures.

Contribution

It defines a new algebraic structure and demonstrates its application in advanced duality theories and Lie algebra representations.

Findings

Established a higher level mixed Schur-Weyl duality for gl_N.

Proved cyclotomic quotients inherit natural grading.

Demonstrated graded cellular structure in these quotients.

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.