Canonical bases for tensor products and super Kazhdan-Lusztig theory

Abstract

We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based ${\text{U}}^{ı}$-module and a based $\text{U}$-module is a based ${\text{U}}^{ı}$-module. This is then used to formulate a Kazhdan-Lusztig theory for an arbitrary parabolic BGG category $\mathcal{O}$ of the ortho-symplectic Lie superalgebras, extending a main result in [BW13] (arXiv:1310.0103).

v4, 10 pages, to appear in the Journal of Pure and Applied Algebra

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• Canonical bases for tensor products and super Kazhdan-Lusztig theory

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