Given \(a,b,c\in\mathbb{N}_0\) let \(j_{a|c}=j_{a|c}^b\colon R_b\hookrightarrow R_{a+b+c}\) be the algebra homomorphism given by \(x_i\mapsto x_{i+a}\). Given an \(R_m\)-bimodule \(M\) and an \(R_n\)-bimodule \(N\), the tensor product \(M\otimes_kN\) is an \(R_m\otimes R_n\)-bimodule, hence an \(R_{m+n}\)-bimodule via the isomorphism \(j_{0|n}\otimes j_{m|0}\). We call this functorial operation parabolic induction.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2