Representations of the cyclotomic oriented Brauer-Clifford supercategory (Q6597196)

Let \(\mathbf{k}\) be an algebraically closed field with characteristic \(p\not= 2\). Assume that superspaces, superalgebras, supercategories, and functors are all \(\mathbf{k}\)-linear. M. Gao, H. Rui, and L. Song generalize the notion of a weakly triangular decomposition to the super case called a super weakly triangular decomposition. The authors show that the underlying even category of locally finite-dimensional left \(A\)-supermodules is an upper finite fully stratified category if the superalgebra \(A\) admits an upper finite super weakly triangular decomposition. In particular, when \(A\) is the locally unital superalgebra associated with the cyclotomic oriented Brauer-Clifford supercategory, the Grothendieck group of the category of left \(A\)-supermodules admitting finite standard flags has a \(\mathfrak{g}\)-module structure that is isomorphic to the tensor product of an integrable lowest weight and an integrable highest weight \(\mathfrak{g}\) module, where \(\mathfrak{g}\) is the complex Kac-Moody Lie algebra of type \(A^{(2)}_{2\ell}\), respectively, \(B_{\infty}\), if \(p =2\ell +1\), respectively, \(p =0\).