Oscillators from non-semisimple walled Brauer algebras

Sanjaye Ramgoolam, Michał Studziński

The walled Brauer algebras $B_N(m,n)$ govern Schur--Weyl duality for unitary groups $U(N)$ acting on mixed tensor spaces $V_N^{\otimes m}\otimes {\overline{V}}_N^{\otimes n}$ and pla…