Abstract

С использованием подхода Гаутама и Толедано-Ларедо вводятся аналоги категории $\mathfrak O$ для представлений янгиана $Y_\hbar(A(m,n))$ специальной линейной супералгебры Ли и квантовой петлевой супералгебры $U_q(LA(m,n))$. Исследуется связь между ними и сформулирована гипотеза об эквивалентности этих категорий.

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