Schur–Sergeev duality for Ariki–Koike algebras
Tom 176 / 2024
Colloquium Mathematicum 176 (2024), 47-76
MSC: Primary 20C99; Secondary 05A99, 16G99, 20C15
DOI: 10.4064/cm9307-7-2024
Opublikowany online: 2 September 2024
Streszczenie
Let be the quantized enveloping superalgebra of \mathfrak g=\mathfrak{gl}(k_1|\ell_1)\oplus \cdots \oplus \mathfrak{gl}(k_m|\ell_m) and let \mathcal H_{m,n} be the Ariki–Koike algebra. We define a right \mathcal H-action on the n-fold tensor (super) space of the vector representation of U_q(\mathfrak g) and prove Schur–Sergeev duality between U_q(\mathfrak g) and \mathcal H_{m,n}.
